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Bismash Products and Group Algebras

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If you have a question about this talk, please contact Anton Evseev.

We will begin by introducing Hopf algebras together with the easiest examples – group algebras and their duals – before giving an overview of the classification attempt for finite-dimensional complex semisimple Hopf algebras. We will then go on to describe more interesting constructions – bicrossed and bismash products – which can be defined using any finite group with a given factorisation into trivially intersecting subgroups, and explain a way of studying bismash products using character theory. We will look at a particular family of bismash products arising from factorisations of the projective general linear group over a finite field, before examining what happens if the factorized group we started is a) a semidirect product, b) a Frobenius group.

This talk is part of the Junior Algebra and Number Theory seminar series.

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