Hopfian Hecke algebras

Andrew Baker (University of Glasgow)

Wednesday 10th June 16:00-17:00
Maths 311B

Abstract

Hecke operations and algebras first appeared in the context of modular and automorphic forms and were built using pairs of groups $H \leqslant G$ and their group algebras. The idea has evolved and the name is now attached to very wide generalisations. In this talk I will discuss a natural extension to pairs of Hopf algebras.

I will review the classical group version then explain how the Hopf version works, in particular focussing on the case of a finite dimensional pair which forms a Frobenius extension (a relative version of a Frobenius algebra) that includes the group case. However, not all finite dimensional Hopf algebra pairs fit into this pattern but they are Frobenius extensions of the second kind and this leads to a more general notion best thought of in the language of rings with several objects.

There are various ways this might be generalised to infinite dimensional pairs, some of which builds on work of Zhang, Brown and others on homological integrals. If there is time I will briefly discuss this. p>

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