Finite projection monoids
Algebra Seminar
18th February 2025, 4:00 pm – 5:00 pm
Fry Building, 2.04
The theory of finite reflection groups (both real and complex) is a beautiful and very well-studied part of mathematics. In this talk we will consider a generalisation, where we allow generators to be any linear maps (including non-invertible ones) fixing a subspace of codimension 1, and we ask for the monoid they generate to be finite. We will see that many of the nice features of finite reflection groups fail in this more general setting, but there are some interesting examples. I will sketch a classification result for dimension 2 over the complex numbers.
This is a work in progress - I don't yet have many theorems. I would be keen to hear from anyone interested in taking this further.
Organisers: Jack Saunders, Vlad Vankov
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