Luke Kershaw

Modules over Special Biserial Algebras

Special biserial algebras (SB algebras) are a class of finite-dimensional algebras that have often been used as a testing ground for new methods in representation theory. They are comparatively easy to define, and yet have been non-trivial to study; providing a rich source of examples and counterexamples to various ideas.

There are two main classes of indecomposable modules over SB algebras: string modules and band modules. In 2021, Allen introduced a method for encoding string modules in terms of "syllables"; allowing them to be systematically studied using computer algebra tools such as GAP.

In this talk we will show how these ideas can be extended to allow encoding band modules in terms of "syllables" too, and to show how these encodings can be leveraged to prove new theoretical results. No prior knowledge of finite-dimensional algebras will be assumed.