Tame 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 ...

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...

The strong no loop conjecture for special biserial algebras

Let A be a finite dimensional algebra over a field given by a quiver with relations. Let S be a simple A-module with a non-split self-extension, that is, the quiver has a loop at the corresponding vertex. The strong no loop conjecture claims that S is of infinite projective dimension; see [1, 6]. This conjecture remains open except for monomial algebras; see, for example, [2, 6, 8, 11]. Under c...

On Ringel-hall Algebras of Tame Hereditary Algebras

Degenerations for Modules over Representation-finite Biserial Algebras