# Seminars 07/08

Fall 2007 Seminars

**November 28, 2007**

Jason McGraw (MUN) “Simple Lie algebras over a field of positive Characteristic”

**Abstract:**

The simple finite-dimensional Lie algebras over the field of complex numbers (or any algebraically closed field of characteristic zero) were classified by Killing in 1888-1890. The classification depends on the result that the Killing form of such a Lie algebra is nondegenerate. If we consider Lie algebras over an algebraically closed field of positive characteristic, then this result is no longer valid, and there exist simple finite-dimensional Lie algebras that do not have analogues in characteristic zero. The classification of simple finite-dimensional Lie algebras in characteristic p>3 has recently been completed by the efforts of a number of mathematicians since 1930s. In this talk we will introduce a series of Lie algebras that play an important role in this classification, namely, the generalized Jascobson-Witt algebras, which are simple, but have zero Killing form (except for small p).

**October 31, 2007**

Jianjun Chuai,(MUN) “Modules of covariants of a finite linear group”

**Abstract:**

In this talk we will study modules of covariants of a finite linear group. Modules of differential forms are special cases of such modules. We are particularly interested to know when such modules are free over the invariant ring. In this talk I will describe a criterion for the freeness.

Winter 2008 Seminars

**January 30, 2008**

Yuri Bahturin, (MUN) "Group gradings on algebras of finitary linear transformations"

**Abstract:**

In this work we expand the results on gradings of matrix algebras to infinite-dimensional algebras of linear transformations. Among consequences are the applications to the classification of group gradings on finitary simple Lie algebras previously classified in the works of A. Baranov and H. Strade. This is joint work with M. Zaicev.

**January 23, 2008**

Jason McGraw, (MUN) “Simple Lie algebras over a field of positive characteristic II”

Summer 2008 Seminars

**May 20, 2008**

Margaret Beattie, (Mount Allison University) “The general classification problem for Hopf algebras ”

**Abstract:**

In the algebraic study of finite dimensional Hopf algebras over the complex numbers, it is natural to seek classification theorems along the line of those for finite groups. For example, it was shown in 1994 by Yongchang Zhu that a Hopf algebra of prime dimension p is isomorphic to a group algebra. However, even for dimension pq with p and q odd primes, it is not completely known if Hopf algebras of dimension pq are trivial in the sense that they are isomorphic to group algebras or duals of group algebras. This talk will at- tempt to outline some of these problems, give a number of examples, and report on some results which have recently appeared.