H. Krause

H. Krause
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H. Krause
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Mathematics - Representation Theory (40)
 
Mathematics - Category Theory (17)
 
Mathematics - Rings and Algebras (10)
 
Mathematics - Commutative Algebra (9)
 
Mathematics - Algebraic Topology (8)
 
Mathematics - Algebraic Geometry (4)
 
Mathematics - K-Theory and Homology (4)
 
Mathematics - Combinatorics (3)
 
Mathematics - Group Theory (2)
 
Physics - Instrumentation and Detectors (2)
 
Mathematics - Logic (1)
 
Physics - Mesoscopic Systems and Quantum Hall Effect (1)
 
Physics - Atomic Physics (1)
 
Physics - Accelerator Physics (1)
 
Nuclear Experiment (1)

Publications Authored By H. Krause

For abelian length categories the borderline between finite and infinite representation type is discussed. Characterisations of finite representation type are extended to length categories of infinite height, and the minimal length categories of infinite height are described. Read More

Given a tensor-triangulated category $T$, we prove that every flat tensor-idempotent in the module category over $T^c$ (the compacts) comes from a unique smashing ideal in $T$. We deduce that the lattice of smashing ideals forms a frame. Read More

A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander-Reiten triangles for the $\mathfrak{p}$-local and $\mathfrak{p}$-torsion subcategories of the stable category, for each homogeneous prime ideal $\mathfrak{p}$ in the cohomology ring of the group scheme. Read More

2016Aug
Affiliations: 1Physikalisches Institut, Ruprecht-Karls-Universität, Heidelberg, Germany, 2Institut für Physik, Johannes Gutenberg-Universität, Mainz, Germany, 3Institut für Physik, Johannes Gutenberg-Universität, Mainz, Germany, 4Van Swinderen Institute, University of Groningen, The Netherlands, 5Institut für Physik, Johannes Gutenberg-Universität, Mainz, Germany, 6Van Swinderen Institute, University of Groningen, The Netherlands, 7Institut für Physik, Johannes Gutenberg-Universität, Mainz, Germany, 8Peter Grünberg Institute, Forschungszentrum Jülich, Germany, 9Peter Grünberg Institute, Forschungszentrum Jülich, Germany, 10Institut für Physik, Johannes Gutenberg-Universität, Mainz, Germany, 11Physikalisches Institut, Ruprecht-Karls-Universität, Heidelberg, Germany, 12Institut für Physik, Johannes Gutenberg-Universität, Mainz, Germany, 13Institut für Physik, Johannes Gutenberg-Universität, Mainz, Germany, 14Van Swinderen Institute, University of Groningen, The Netherlands, 15Institut für Physik, Johannes Gutenberg-Universität, Mainz, Germany

We report on precise measurements of magnetic field gradients extracted from transverse relaxation rates of precessing spin samples. The experimental approach is based on the free precession of gaseous, nuclear spin polarized $^3$He and $^{129}$Xe atoms in a spherical cell inside a magnetic guiding field of about 400 nT using LT$_C$ SQUIDs as low-noise magnetic flux detectors. The transverse relaxation rates of both spin species are simultaneously monitored as magnetic field gradients are varied. Read More

A set valued representation of the Kronecker quiver is nothing but a quiver. We apply the forgetful functor from vector spaces to sets and compare linear with set valued representations of the Kronecker quiver. Read More

Plasma-enhanced chemical vapor deposition of thin a-Si:H layers on transferred large area graphene is investigated. Radio frequency (RF, 13.56 MHz) and very high frequency (VHF, 140 MHz) plasma processes are compared. Read More

Auslander-Reiten duality for module categories is generalised to Grothendieck abelian categories that have a sufficient supply of finitely presented objects. It is shown that Auslander-Reiten duality amounts to the fact that the functor Ext^1(C,-) into modules over the endomorphism ring of C admits a partially defined right adjoint when C is a finitely presented object. This result seems to be new even for module categories. Read More

For a finite group scheme, the subadditive functions on finite dimensional representations are studied. It is shown that the projective variety of the cohomology ring can be recovered from the equivalence classes of subadditive functions. Using Crawley-Boevey's correspondence between subadditive functions and endofinite modules, we obtain an equivalence relation on the set of point modules introduced in our joint work with Iyengar and Pevtsova. Read More

The Hom closed colocalising subcategories of the stable module category of a finite group scheme are classified. This complements the classification of the tensor closed localising subcategories in our previous work. Both classifications involve pi-points in the sense of Friedlander and Pevtsova. Read More

2016Mar
Authors: M. Arenz, M. Babutzka, M. Bahr, J. P. Barrett, S. Bauer, M. Beck, A. Beglarian, J. Behrens, T. Bergmann, U. Besserer, J. Blümer, L. I. Bodine, K. Bokeloh, J. Bonn, B. Bornschein, L. Bornschein, S. Büsch, T. H. Burritt, S. Chilingaryan, T. J. Corona, L. De Viveiros, P. J. Doe, O. Dragoun, G. Drexlin, S. Dyba, S. Ebenhöch, K. Eitel, E. Ellinger, S. Enomoto, M. Erhard, D. Eversheim, M. Fedkevych, A. Felden, S. Fischer, J. A. Formaggio, F. Fränkle, D. Furse, M. Ghilea, W. Gil, F. Glück, A. Gonzalez Urena, S. Görhardt, S. Groh, S. Grohmann, R. Grössle, R. Gumbsheimer, M. Hackenjos, V. Hannen, F. Harms, N. Hauÿmann, F. Heizmann, K. Helbing, W. Herz, S. Hickford, D. Hilk, B. Hillen, T. Höhn, B. Holzapfel, M. Hötzel, M. A. Howe, A. Huber, A. Jansen, N. Kernert, L. Kippenbrock, M. Kleesiek, M. Klein, A. Kopmann, A. Kosmider, A. Kovalík, B. Krasch, M. Kraus, H. Krause, M. Krause, L. Kuckert, B. Kuffner, L. La Cascio, O. Lebeda, B. Leiber, J. Letnev, V. M. Lobashev, A. Lokhov, E. Malcherek, M. Mark, E. L. Martin, S. Mertens, S. Mirz, B. Monreal, K. Müller, M. Neuberger, H. Neumann, S. Niemes, M. Noe, N. S. Oblath, A. Off, H. -W. Ortjohann, A. Osipowicz, E. Otten, D. S. Parno, P. Plischke, A. W. P. Poon, M. Prall, F. Priester, P. C. -O. Ranitzsch, J. Reich, O. Rest, R. G. H. Robertson, M. Röllig, S. Rosendahl, S. Rupp, M. Rysavy, K. Schlösser, M. Schlösser, K. Schönung, M. Schrank, J. Schwarz, W. Seiler, H. Seitz-Moskaliuk, J. Sentkerestiova, A. Skasyrskaya, M. Slezak, A. Spalek, M. Steidl, N. Steinbrink, M. Sturm, M. Suesser, H. H. Telle, T. Thümmler, N. Titov, I. Tkachev, N. Trost, A. Unru, K. Valerius, D. Venos, R. Vianden, S. Vöcking, B. L. Wall, N. Wandkowsky, M. Weber, C. Weinheimer, C. Weiss, S. Welte, J. Wendel, K. L. Wierman, J. F. Wilkerson, D. Winzen, J. Wolf, S. Wüstling, M. Zacher, S. Zadoroghny, M. Zboril

The KATRIN experiment will probe the neutrino mass by measuring the beta-electron energy spectrum near the endpoint of tritium beta-decay. An integral energy analysis will be performed by an electro-static spectrometer (Main Spectrometer), an ultra-high vacuum vessel with a length of 23.2 m, a volume of 1240 m^3, and a complex inner electrode system with about 120000 individual parts. Read More

The tensor ideal localising subcategories of the stable module category of all, including infinite dimensional, representations of a finite group scheme over a field of positive characteristic are classified. Various applications concerning the structure of the stable module category and the behavior of support and cosupport under restriction and induction are presented. Read More

We provide several equivalent descriptions of a highest weight category using recollements of abelian categories. Also, we explain the connection between sequences of standard and exceptional objects. Read More

We introduce the notion of $\pi$-cosupport as a new tool for the stable module category of a finite group scheme. In the case of a finite group, we use this to give a new proof of the classification of tensor ideal localising subcategories. In a sequel to this paper, we carry out the corresponding classification for finite group schemes. Read More

2015Apr
Affiliations: 1JEDI collaboration, 2JEDI collaboration, 3JEDI collaboration, 4JEDI collaboration, 5JEDI collaboration, 6JEDI collaboration, 7JEDI collaboration, 8JEDI collaboration, 9JEDI collaboration, 10JEDI collaboration, 11JEDI collaboration, 12JEDI collaboration, 13JEDI collaboration, 14JEDI collaboration, 15JEDI collaboration, 16JEDI collaboration, 17JEDI collaboration, 18JEDI collaboration, 19JEDI collaboration, 20JEDI collaboration, 21JEDI collaboration, 22JEDI collaboration, 23JEDI collaboration, 24JEDI collaboration, 25JEDI collaboration, 26JEDI collaboration, 27JEDI collaboration, 28JEDI collaboration, 29JEDI collaboration, 30JEDI collaboration, 31JEDI collaboration, 32JEDI collaboration, 33JEDI collaboration, 34JEDI collaboration, 35JEDI collaboration, 36JEDI collaboration, 37JEDI collaboration, 38JEDI collaboration, 39JEDI collaboration, 40JEDI collaboration, 41JEDI collaboration, 42JEDI collaboration, 43JEDI collaboration, 44JEDI collaboration, 45JEDI collaboration, 46JEDI collaboration, 47JEDI collaboration, 48JEDI collaboration, 49JEDI collaboration, 50JEDI collaboration, 51JEDI collaboration, 52JEDI collaboration, 53JEDI collaboration, 54JEDI collaboration, 55JEDI collaboration, 56JEDI collaboration, 57JEDI collaboration, 58JEDI collaboration, 59JEDI collaboration, 60JEDI collaboration, 61JEDI collaboration, 62JEDI collaboration, 63JEDI collaboration, 64JEDI collaboration, 65JEDI collaboration, 66JEDI collaboration, 67JEDI collaboration, 68JEDI collaboration, 69JEDI collaboration, 70JEDI collaboration, 71JEDI collaboration, 72JEDI collaboration, 73JEDI collaboration, 74JEDI collaboration, 75JEDI collaboration, 76JEDI collaboration, 77JEDI collaboration, 78JEDI collaboration, 79JEDI collaboration, 80JEDI collaboration, 81JEDI collaboration, 82JEDI collaboration, 83JEDI collaboration, 84JEDI collaboration, 85JEDI collaboration, 86JEDI collaboration, 87JEDI collaboration, 88JEDI collaboration, 89JEDI collaboration, 90JEDI collaboration, 91JEDI collaboration, 92JEDI collaboration, 93JEDI collaboration, 94JEDI collaboration, 95JEDI collaboration, 96JEDI collaboration, 97JEDI collaboration, 98JEDI collaboration, 99JEDI collaboration, 100JEDI collaboration, 101JEDI collaboration

A new method to determine the spin tune is described and tested. In an ideal planar magnetic ring, the spin tune - defined as the number of spin precessions per turn - is given by $\nu_s = \gamma G$ (gamma is the Lorentz factor, $G$ the magnetic anomaly). For 970 MeV/c deuterons coherently precessing with a frequency of ~120 kHz in the Cooler Synchrotron COSY, the spin tune is deduced from the up-down asymmetry of deuteron carbon scattering. Read More

This note provides a self-contained exposition of the proof of the artinian conjecture, following closely Djament's Bourbaki lecture. The original proof is due to Putman, Sam, and Snowden. Read More

Krull-Schmidt categories are additive categories such that each object decomposes into a finite direct sum of indecomposable objects having local endomorphism rings. We provide a self-contained introduction which is based on the concept of a projective cover. Read More

Auslander's formula shows that any abelian category C is equivalent to the category of coherent functors on C modulo the Serre subcategory of all effaceable functors. We establish a derived version of this equivalence. This amounts to showing that the homotopy category of injective objects of some appropriate Grothendieck abelian category (the category of ind-objects of C) is compactly generated and that the full subcategory of compact objects is equivalent to the bounded derived category of C. Read More

Highest weight categories are described in terms of standard objects and recollements of abelian categories, working over an arbitrary commutative base ring. Then the highest weight structure for categories of strict polynomial functors is explained, using the theory of Schur and Weyl functors. A consequence is the well-known fact that Schur algebras are quasi-hereditary. Read More

We describe a procedure for constructing morphisms in additive categories, combining Auslander's concept of a morphism determined by an object with the existence of flat covers. Also, we show how flat covers are turned into projective covers, and we interprete these constructions in terms of adjoint functors. Read More

We compute the Krull-Gabriel dimension of the category of perfect complexes for finite dimensional algebras which are derived discrete. Read More

Polynomial representations of general linear groups and modules over Schur algebras are compared. We work over an arbitrary commutative ring and show that Schur-Weyl duality is the key for an equivalence between both categories. Read More

We present a categorification of the non-crossing partitions given by crystallographic Coxeter groups. This involves a category of certain bilinear lattices, which are essentially determined by a symmetrisable generalised Cartan matrix together with a particular choice of a Coxeter element. Examples arise from Grothendieck groups of hereditary artin algebras. Read More

Local cohomology functors are constructed for the category of cohomological functors on an essentially small triangulated category T equipped with an action of a commutative noetherian ring. This is used to establish a local-global principle and to develop a notion of stratification, for T and the cohomological functors on it, analogous to such concepts for compactly generated triangulated categories. Read More

We discuss the notion of strongly unbounded type for abelian length categories; this is closely related to the Second Brauer-Thrall Conjecture for artin algebras. A new ingredient is the space of characters in the sense of Crawley-Boevey. Read More

We study certain integer valued length functions on triangulated categories and establish a correspondence between such functions and cohomological functors taking values in the category of finite length modules over some ring. The irreducible cohomological functions form a topological space. We discuss its basic properties and include explicit calculations for the category of perfect complexes over some specific rings. Read More

We develop a suitable version of the stable module category of a finite group G over an arbitrary commutative ring k. The purpose of the construction is to produce a compactly generated triangulated category whose compact objects are the finitely presented kG-modules. The main idea is to form a localisation of the usual version of the stable module category with respect to the filtered colimits of weakly injective modules. Read More

This is a report on recent work of Chalupnik and Touze. We explain the Koszul duality for the category of strict polynomial functors and make explicit the underlying monoidal structure which seems to be of independent interest. Then we connect this to Ringel duality for Schur algebras and describe Serre duality for strict polynomial functors. Read More

Inclusion preserving maps from modules over an Artin algebra to complete partially ordered sets are studied. This yields a filtration of the Ziegler spectrum which is indexed by all Gabriel-Roiter measures. Another application is a compactness result for the set of subcategories of finitely presented modules that are closed under submodules. Read More

For an exact category having enough projective objects, we establish a bijection between thick subcategories containing the projective objects and thick subcategories of the stable derived category. Using this bijection we classify thick subcategories of finitely generated modules over local complete intersections and produce generators for the category of coherent sheaves on a separated noetherian scheme with an ample family. Read More

The concept of a morphism determined by an object provides a method to construct or classify morphisms in a fixed category. We show that this works particularly well for triangulated categories having Serre duality. Another application of this concept arises from a reformulation of Freyd's generating hypothesis. Read More

The localising subcategories of the derived category of the cochains on the classifying space of a finite group are classified. They are in one to one correspondence with the subsets of the set of homogeneous prime ideals of the cohomology ring $H^*(G,k)$. Read More

These notes give an introduction to the Gabriel-Roiter measure of a finite dimensional algebra. They are based on a series of four lectures at the "Advanced School and Conference on Representation Theory and Related Topics" in Trieste (ICTP, January 2006). Read More

For a tensor triangulated category which is well generated in the sense of Neeman, it is shown that the collection of Bousfield classes forms a set. This set has a natural structure of a complete lattice which is then studied, using the notions of stratification and support. Read More

This survey article is intended as an introduction to the recent categorical classification theorems of the three authors, restricting to the special case of the category of modules for a finite group. Read More

The basic properties of locally finite triangulated categories are discussed. The focus is on Auslander--Reiten theory and the lattice of thick subcategories. Read More

Expansions of abelian categories are introduced. These are certain functors between abelian categories and provide a tool for induction/reduction arguments. Expansions arise naturally in the study of coherent sheaves on weighted projective lines; this is illustrated by various applications. Read More

The Hom closed colocalizing subcategories of the stable module category of a finite group are classified. Along the way, the colocalizing subcategories of the homotopy category of injectives over an exterior algebra, and the derived category of a formal commutative differential graded algebra, are classified. To this end, and with an eye towards future applications, a notion of local homology and cosupport for triangulated categories is developed, building on earlier work of the authors on local cohomology and support. Read More

We provide a criterion for the existence of right approximations in cocomplete additive categories; it is a straightforward generalisation of a result due to El Bashir. This criterion is used to construct adjoint functors in homotopy categories. Applications include the study of (pure) derived categories. Read More

These notes provide a description of the abelian categories that arise as categories of coherent sheaves on weighted projective lines. Two different approaches are presented: one is based on a list of axioms and the other yields a description in terms of expansions of abelian categories. A weighted projective line is obtained from a projective line by inserting finitely many weights. Read More

A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences which follow when T is stratified by R. Among them are a classification of the localizing subcategories of T in terms of subsets of the set of prime ideals in R; a classification of the thick subcategories of the subcategory of compact objects in T; and results concerning the support of the R-module of homomorphisms Hom_T^*(C,D) leading to an analogue of the tensor product theorem for support varieties of modular representation of groups. Read More

We discuss some basic properties of the graded center of a triangulated category and compute examples arising in representation theory of finite dimensional algebras. Read More

For the module category of a hereditary ring, the Ext-orthogonal pairs of subcategories are studied. For each Ext-orthogonal pair that is generated by a single module, a 5-term exact sequence is constructed. The pairs of finite type are characterized and two consequences for the class of hereditary rings are established: homological epimorphisms and universal localizations coincide, and the telescope conjecture for the derived category holds true. Read More

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context. Others include new proofs of the tensor product theorem and of the classification of thick subcategories of the finitely generated modules which avoid the use of cyclic shifted subgroups. Read More

These notes provide an introduction to the theory of localization for triangulated categories. Localization is a machinery to formally invert morphisms in a category. We explain this formalism in some detail and we show how it is applied to triangulated categories. Read More

These are the notes for a course on representations of quivers for second year students in Paderborn in summer 2007. My aim was to provide a basic introduction without using any advanced methods. It turns out that a good knowledge of linear algebra is sufficient for proving Gabriel's theorem. Read More

Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for the representation dimensions of certain Artin algebras. Read More

For a commutative noetherian ring A, we compare the support of a complex of A-modules with the support of its cohomology. This leads to a classification of all full subcategories of A-modules which are thick (that is, closed under taking kernels, cokernels, and extensions) and closed under taking direct sums. Read More

We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local cohomology functors on triangulated categories, with respect to a central ring of operators. Suitably specialized one recovers, for example, the theory for commutative noetherian rings due to Foxby and Neeman, the theory of Avramov and Buchweitz for complete intersection local rings, and varieties for representations of finite groups according to Benson, Carlson, and Rickard. Read More

Given a cohomological functor from a triangulated category to an abelian category, we construct under appropriate assumptions for any localization functor of the abelian category a lift to a localization functor of the triangulated category. This discussion of Bousfield localization is combined with a basic introduction to the concept of localization for arbitrary categories. Read More