##### Department of Mathematics,

University of California San Diego

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### Algebra Seminar

## Gene Abrams

#### University of Colorado at Colorado Springs

## Leavitt path algebras: connections and applications

##### Abstract:

\indent Since 2005 a class of algebras, the 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. \indent I'll briefly describe some results of the expected form, namely, results of the form: $E$ has property $P$ if and only if $L_K(E)$ has property $P'$. \indent 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 or primitive algebras; about $C*-$algebras; and about Lie algebras have been gleaned from these structures.

Host: Dan Rogalski

### March 7, 2011

### 2:00 PM

### AP&M 7321

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