Events Calendar

Algebra Seminar (Double Header) G. Abrams & B. Chin

Gene Abrams, University of Colorado, Colorado Springs,

Abstract:

Since 2005 a class of algebras, the {it Leavitt path algebras} $L_K(E)$ (for $K$ any field and $E$ any directed graph), has been a focus of investigation by both algebraists and $C^*$-analysts.  In this talk I'll define these algebras, and give some insight regarding the ideas which prompted the initial description of these structures.

I'll briefly describe some results of the expected form, namely, results of the form: $E$  has property ${mathcal P}$  $Leftrightarrow$    $L_K(E)$  has property ${mathcal P}'$.

However, the main goal of the talk will be to show how Leavitt path  algebras have been used to answer various questions outside the subject per se.  For example, results about von Neumann regular rings; about prime / primitive algebras; about $C^*$-algebras; about  finitely presented simple groups; and about  Lie algebras have been gleaned from these structures.