Event Type:

Department Colloquium

Date/Time:

Monday, May 17, 2010 - 09:00

Location:

Kidder 350

Guest Speaker:

Darren Funk-Neubauer

Institution:

Colorado State University - Pueblo

Abstract:

Whether it be groups, rings, associative algebras, Lie algebras, or modules algebraists often try to understand algebraic structures by considering the idea of simplicity. Deciding how to define what it means for an algebraic structure to be simple and then characterizing when a structure is simple is a common theme in many areas of algebra research. This talk will discuss how simplicity is defined, explain why algebraists care about simplicity, and examine some simplicity results in different areas of algebra.

In particular, the talk will focus on Leavitt (path) algebras (a class of associative algebras) and Lie algebras. Leavitt algebras were originally developed in the 1960s in response to ring theoretic research questions. In the 2000s research in these algebras has been revived through the study of the more general Leavitt path algebras. Leavitt path algebras are algebras arising from directed graphs and the simplicity of these algebras is determined by the combinatorics of the graph. On the other hand, the study of Lie algebras have been around since the 1880s and there are many, many simplicity results known.

Until very recently Leavitt (path) algebras and Lie algebras were unrelated. Only in the last few years has research begun connecting the two. This talk will conclude with a description of some simplicity results connecting Leavitt (path) algebras and Lie algebras. These results are joint work between the speaker and Gene Abrams of University of Colorado-Colorado Springs.

Special care will be taken to ensure that following this talk requires no prerequisite knowledge of Lie algebras. The talk will only assume the audience has a basic knowledge of ring theory at the level of a first year graduate course in algebra.