**SMS scnews item created by James East at Mon 22 Jun 2009 1345**

Type: Seminar

Distribution: World

Expiry: 26 Jun 2009

**Calendar1: 26 Jun 2009 1205-1255**

**CalLoc1: Carslaw 375**

Auth: jamese@bari.maths.usyd.edu.au

### Algebra Seminar

# Group gradings on finite-dimensional simple Lie algebras

### Mikhail Kotchetov

#### Friday June 26, 12:05--12:55pm, Carslaw 375

###### Abstract

Group gradings on algebras, especially simple algebras, have been extensively
studied since the 1960s. In particular, gradings on Lie algebras arise in the
theory of symmetric spaces, Kac-Moody algebras, and Lie coloralgebras. In the
context of simple Lie algebras, it suffices to consider only gradings by
abelian groups (since the support of any grading generates an abelian group).
In 1968, V. Kac classified all gradings by cyclic groups on finite-dimensional
simple Lie algebras. The study of gradings by arbitrary abelian groups on these
algebras was started in the works by J. Patera and H. Zassenhaus in the late
1980s. We will discuss recent progress in this area.

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After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

James East jamese@maths.usyd.edu.au