Some generalisations of Frobenius algebras: the algebra behind homotopy QFTs

Timothy Porter, University of Bangor. Part of the algebra seminar series.

Frobenius algebras arise naturally in group representation theory, and have several equivalent formulations. Looking at them from a categorical /string diagram perspective it is clear that if one thickens them up a bit, diagrams for `Frobenius objects' look very like the diagrams from Topological QFTs. I will go over these ideas recalling now `classical results' on 1+1 TQFTs and then generalise in several different ways to get analogues of Frobenius algebras for crossed modules of groups which are interesting in their own right. The topology mirrors the algebra and vice versa.

Timothy Porter, University of Bangor