In joint work with Sibylle Schroll (Univ. of Leicester), we introduce a generalization of Brauer graph algebras which we call Brauer configuration algebras. These will be defined in the talk. Brauer graph algebras are the symmetric special biserial algebras and are currently under active investigation. Defining an algebra KQ/I to be special multiserial if, for each arrow a in the quiver, there is at most one arrow one arrow b such that ab ∉ I and at most one arrow c such that ca ∉ I, we show that KQ/I is a symmetric multiserial algebra if and only if it is a Brauer configuration algebra.
An algebra is called multiserial if the Jacobson radical as a left and as a right module is a Σi Ui of uniserial modules Ui such that the intersection of any two is either (0) or a simple module. We will present a number of results, including the following:
(1) A special multiserial algebra is multiserial.
(2) The trivial extension of an almost gentle algebra by its dual is a Brauer configuration
algebra.
(3) Every symmetric radical cubed zero algebra is a Brauer configuration algebra.
(4) Every special multiserial algebra is the quotient of a Brauer configuration algebra.
We say a module M is multiserial if rad(M) is a sum Σi Ui of uniserial modules Ui such that the intersection of any two is either (0) or a simple module. Although special multiserial algebras are usually of wild representation type, we have the following surprising result which indicates that although wild, the representation theory is worth studying.
Theorem If Λ is a special multiserial algebra and M is a finitely generated Λ-module, then M is a multiserial module.
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