Linear algebra, quiver representations and quantum groups

Abstract:

A quiver is a (finite) directed graph. A representation of a quiver is to attach every vertex with a vector space and attach every arrow with a linear transformation.

Thus, Linear Algebra is the representation theory of the quiver of one vertex and one arrow (i.e., a loop). When a quiver is a so-called Dynkin quiver, its representations can be explicitly classified in terms of roots, a notion which is fundamental to Lie theory.

I will use some examples to illustrate the theory and will mention one important application to the theory of quantum groups.