Multiserial and special multiserial algebras and their representations

Edward L. Green, Sibylle Schroll

Published 2015-09-01Version 1

We define multiserial and special multiserial algebras. These algebras are generalizations of two well-studied classes of algebras: biserial algebras and special biserial algebras. We call a module multiserial if its radical modulo its socle is a direct sum of uniserial modules. We show that all finitely generated modules over a special multiserial algebra are multiserial. In particular, this imples that, in analogy to special biserial algebras being biserial, special multiserial algebras are multiserial. We then show that the class of symmetric special multiserial algebras coincides with the class of Brauer configuration algebras, where the latter are a generalization of Brauer graph algebras. We end by showing that any symmetric algebra with radical cube zero is special multiserial and so, in particular, it is a Brauer configuration algebra.