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Algebra & Geometry Seminar

Monday, September 27th, 2021

Time: 4:30 p.m.  Place: Online via Zoom (contact Kaveh Mousavand for Zoom link)

Speaker: Charles Paquette (Royal Military College & ³ÉÈË´óƬ)

Title: Simple representations over free products of semi-simple algebras via quivers.

Abstract: This is a report on joint work with Andrew Buchanan, Ivan Dimitrov, Olivia Grace, David Wehlau and Tianyuan Xu. We consider a free product $A$ of semi-simple $\mathbb{K}$-algebras over an algebraically closed field and show how representation theory of a suitable finite acyclic quiver $Q$ can be used to understand the representation theory of $A$. In particular, we show that the simple $A$-modules correspond to stable representations of $Q$ for some stability parameter. We apply this to the representation theory of free products of finite groups.

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