The Graduate Student Seminar

is pleased to announce a lecture by

Eloy Lopez

on

Quivers

Tuesday, October 17 at 4pm in JR 202

Abstract:

This talk is based on the study of two kinds of representation theory, namely, quiver representation theory and Lie algebra representation theory. By looking at some simple examples, we demonstrate the connection between these two topics.

In particular, we present a demostration of Kac's theorem by showing the link between the so-called 2-Kronecker quiver and the Lie algebra $sl_2(k)$. First, we identify isomorphism classes of simple indecomposable representations of this quiver and relate them to equivalence classes of simple indecomposable representations of $sl_2(k)$. Then we demonstrate the relation between the dimension of indecomposable representations of quivers and the roots of Lie algebras.

Eloy Lopez is a first year graduate student at CSUN. In summer 2006 he participated in the I.R.E.S. work shop in Brazil. This lecture is based on work completed in this work shop.