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 and up to stable equivalence of Morita type. This includes the algebras of [Bocian-Holm-Skowro\'nski, J. Pure Appl. Algebra 2004], where they study the weakly symmetric algebras of Euclidean type, as well as some algebras of dihedral type.

Mots clés: Special biserial algebra; derived equivalence; stable equivalence of Morita type; generalised Brauer tree algebra

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. Proceedings of the Edinburgh Mathematical Society, 2015, 58, pp.739-767. ⟨hal-00700438v3⟩