Self-equivalences of the derived category of Brauer tree algebras with exceptional vertex.
Separable functors in corings.
Separable K-linear categories
We define and investigate separable K-linear categories. We show that such a category C is locally finite and that every left C-module is projective. We apply our main results to characterize separable linear categories that are spanned by groupoids or delta categories.
Smash products for -sets, Clifford theory and duality theorems.
Stable equivalences of Morita type for self-injective algebras and p-groups.
Standardly stratified split and lower triangular algebras
In the first part, we study algebras A such that A = R ⨿ I, where R is a subalgebra and I a two-sided nilpotent ideal. Under certain conditions on I, we show that A is standardly stratified if and only if R is standardly stratified. Next, for , we show that A is standardly stratified if and only if the algebra R = U × V is standardly stratified and is a good V-module.
Strict Mittag-Leffler conditions and locally split morphisms
In this paper, we prove that any pure submodule of a strict Mittag-Leffler module is a locally split submodule. As applications, we discuss some relations between locally split monomorphisms and locally split epimorphisms and give a partial answer to the open problem whether Gorenstein projective modules are Ding projective.
Strongly groupoid graded rings and cohomology
We interpret the collection of invertible bimodules as a groupoid and call it the Picard groupoid. We use this groupoid to generalize the classical construction of crossed products to what we call groupoid crossed products, and show that these coincide with the class of strongly groupoid graded rings. We then use groupoid crossed products to obtain a generalization from the group graded situation to the groupoid graded case of the bijection from a second cohomology group, defined by the grading...
Structure of additive categories
Subcategories of the derived category and cotilting complexes
We show that there is a one-to-one correspondence between basic cotilting complexes and certain contravariantly finite subcategories of the bounded derived category of an artin algebra. This is a triangulated version of a result by Auslander and Reiten. We use this to find an existence criterion for complements to exceptional complexes.
Substructures and radicals of Morita contexts for near-rings and Morita near-rings.
Sur la dualité locale
Une construction explicite et élémentaire de l’homomorphisme trace pour les applications analytiques locales de type fini entre des espaces normaux est donnée. On généralise le théorème de dualité locale dans le cas où l’anneau local à la source est un anneau de factorisation unique. Des exemples et des applications sont donnés.
Symmetric Hochschild extension algebras
By an extension algebra of a finite-dimensional K-algebra A we mean a Hochschild extension algebra of A by the dual A-bimodule . We study the problem of when extension algebras of a K-algebra A are symmetric. (1) For an algebra A= KQ/I with an arbitrary finite quiver Q, we show a sufficient condition in terms of a 2-cocycle for an extension algebra to be symmetric. (2) Let L be a finite extension field of K. By using a given 2-cocycle of the K-algebra L, we construct a 2-cocycle of the K-algebra...
Symmetric special biserial algebras of euclidean type
We classify (up to Morita equivalence) all symmetric special biserial algebras of Euclidean type, by algebras arising from Brauer graphs.