Classification of symmetric special biserial algebras with at most one non-uniserial indecomposable projective

Nicole Snashall (1) , Rachel Taillefer (2)

1 Department of Mathematics [Leicester]
2 LMBP - Laboratoire de Mathématiques Blaise Pascal

We consider a natural generalisation of symmetric Nakayama algebras, namely, symmetric special biserial algebras with at most one non-uniserial indecomposable projective module. We describe the basic algebras explicitly by quiver and relations, then classify them up to derived equivalence. This includes the algebras of [Bocian-Holm-Skowro\'nski, J. Pure Appl. Algebra 2004], where they study the weakly symmetric algebras of Euclidean type.

Mots clés: Special biserial algebras; Nakayama algebras; Brauer graph algebras; Hochschild cohomology; Derived equivalence

Domaines: Théorie des représentations [math.RT]; K-théorie et homologie [math.KT]

Nicole Snashall, Rachel Taillefer. Classification of symmetric special biserial algebras with at most one non-uniserial indecomposable projective. 2012. ⟨hal-00700438v1⟩