Selfinjective biserial standard algebras

The Derived Equivalence Classification of Representation-finite Selfinjective Standard Algebras

Selfinjective Koszul Algebras

The study of Koszul algebras and their representations has accelerated significantly in the last few years. They have been used in Topology, Algebraic Geometry and Commutative Algebra and they are used more and more frequently in Representation Theory, see for instance [BGS],[GTM],[M],[MZ] and [R]. The aim of this paper is to present some of the results presented by the second author at the Lum...

Derived equivalence of symmetric special biserial algebras

We introduce Brauer complex of symmetric SB-algebra, and reformulate in terms of Brauer complex the so far known invariants of stable and derived equivalence of symmetric SB-algebras. In particular, the genus of Brauer complex turns out to be invariant under derived equivalence. We study transformations of Brauer complexes which preserve class of derived equivalence. Additionally, we establish ...

Tilting Selfinjective Algebras and Gorenstein Orders

BY Rickard's fundamental theorem [8], the rings which are derived equivalent to a ring A are precisely the endomorphism rings of tilting complexes over A. A tilting complex T is a finitely generated complex of finitely generated projective modules, which does not admit selfextensions and which has the property that the smallest triangulated subcategory of D(A) which contains T also contains all...

MAXIMAL n-ORTHOGONAL MODULES FOR SELFINJECTIVE ALGEBRAS

Let A be a finite-dimensional selfinjective algebra. We show that, for any n ≥ 1, maximal n-orthogonal A-modules (in the sense of Iyama) rarely exist. More precisely, we prove that if A admits a maximal n-orthogonal module, then all A-modules are of complexity at most 1.