Skew Hecke Algebras
James Waldron (University of Newcastle)
Wednesday 28th January 16:00-17:00
Maths 311B
Abstract
Let G be a finite group, H a subgroup of G, and R a ring equipped with an action of G. To this data one can associate a 'skew Hecke ring'. Variants of this construction have appeared in topology in work of Baker, and in mathematical physics in the theory of quantum reference frames.
I will explain a number of common generalisations to skew Hecke rings of basic results concerning skew group rings and Hecke rings of finite groups. In particular, skew Hecke rings admit a double coset decomposition, are isomorphic to certain rings of invariants, and behave nicely under various group-theoretic constructions. If there is time I will discuss modules over skew Hecke rings and homological properties, and some potential links to other areas.
Everything is joint work with Leon Loveridge at USN Norway.
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