On Bernstein-Gelfand-Gelfand equivalence and tilting theory
On induced modules over strongly group-graded algebras.
On intecomposable Lattices over Twisted group rings
On selfinjective algebras of Euclidean type
On tame repetitive algebras
On the density of fiber sum factors.
On the existence of almost split sequences in subcategories
On the representation type of triangular matrix algebras over special algebras
On the structure of Calabi-Yau categories with a cluster tilting subcategory.
Projective homomorphisms and extensions of lattices.
Pseudo-représentations.
Quasi-hereditary algebras with a duality.
Radicals of symmetric cellular algebras
For a symmetric cellular algebra, we study properties of the dual basis of a cellular basis first. Then a nilpotent ideal is constructed. The ideal connects the radicals of cell modules with the radical of the algebra. It also yields some information on the dimensions of simple modules. As a by-product, we obtain some equivalent conditions for a finite-dimensional symmetric cellular algebra to be semisimple.
Representation fields for commutative orders
A representation field for a non-maximal order in a central simple algebra is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders containing a copy of . Not every non-maximal order has a representation field. In this work we prove that every commutative order has a representation field and give a formula for it. The main result is proved for central simple algebras over arbitrary global fields.
Representation fields for cyclic orders
Representation theory of two-dimensionalbrauer graph rings
We consider a class of two-dimensional non-commutative Cohen-Macaulay rings to which a Brauer graph, that is, a finite graph endowed with a cyclic ordering of edges at any vertex, can be associated in a natural way. Some orders Λ over a two-dimensional regular local ring are of this type. They arise, e.g., as certain blocks of Hecke algebras over the completion of at (p,q-1) for some rational prime . For such orders Λ, a class of indecomposable maximal Cohen-Macaulay modules (see introduction)...
Representation-finite triangular algebras form an open scheme
Let V be a valuation ring in an algebraically closed field K with the residue field R. Assume that A is a V-order such that the R-algebra Ā obtained from A by reduction modulo the radical of V is triangular and representation-finite. Then the K-algebra KA ≅ A ⊗V is again triangular and representation-finite. It follows by the van den Dries’s test that triangular representation-finite algebras form an open scheme.
Self-equivalences of the derived category of Brauer tree algebras with exceptional vertex.
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.
Symmetrische Algebren mit endlich vielen unzerlegbaren Darstellungen. II.