On Representation-Finite Gendo-Symmetric Biserial Algebras

Degenerations for Modules over Representation-finite Biserial Algebras

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 ...

The Yoneda Algebras of Symmetric Special Biserial Algebras Are Finitely Generated

By using the Benson–Carlson diagrammatic method, a detailed combinatorial description is given for the syzygies of simple modules over special biserial algebras. With the help of this description, it is proved that the Yoneda algebras of the algebras mentioned above are finitely generated.

On Algebras of Finite Representation Type

Since D. G. Higman proved that bounded representation type and finite representation type are equivalent for group algebras at prime characteristic, there has been a renewed interest in the Brauer-Thrall conjecture that bounded representation type implies finite representation type for arbitrary algebras. The main purpose of this paper is to present a new approach to this conjecture by showing ...

Special biserial algebras with no outer derivations

Let A be a special biserial algebra over an algebraically closed field. We show that the first Hohchshild cohomology group of A with coefficients in the bimodule A vanishes if and only if A is representation finite and simply connected (in the sense of Bongartz and Gabriel), if and only if the Euler characteristic of Q equals the number of indecomposable non uniserial projective injective A-mod...