# Seminars 12/13

**2012/2013 Seminars**

**December 5, 2012**

Hamid Usefi (Memorial University)

"Lie solvable enveloping algebras"

Let L be a restricted Lie algebra with restricted enveloping algebra u(L) over a field of characteristic p>0. The characterization of L when u(L) is Lie solvable was done by Riley and Shalev in case p>2, however the remaining case p=2 remained a subtle problem. In a recent paper joint with Siciliano we tried to tackle this and now we have a complete classification. In this talk, I will try to give an outline of the proof and explain how difficulty arises.

*HH-3017, 1:00-2:00 p.m.*

**November 21, 2012**

Serkan Sütlü (University of New Brunswick, Fredericton)

"Hopf-cyclic cohomology of Lie-Hopf algebras."

A Lie-Hopf algebra is a bicrossed product Hopf algebra obtained from a Lie algebra via semidualization. Illustrating this procedure, we discuss stable-anti-Yetter-Drinfeld (SAYD) modules over Lie-Hopf algebras and Lie algebras. We introduce the notion of coaction of a Lie algebra, and we show that SAYD modules over Lie-Hopf algebras correspond to SAYD modules over the associated Lie algebras. Finally, introducing the cyclic cohomology of a Lie algebra with SAYD coefficients, we discuss a similar correspondence in the level of cohomologies. Explicitly, we show that the Hopf-cyclic cohomology of a Lie-Hopf algebra is the same as the cyclic cohomology of the associated Lie algebra.

*HH-3017, 1:00-2:00 p.m.*

**November 7, 2012**

Mikhail Kotchetov (Memorial University)

"Counting fine gradings on matrix algebras and on classical simple Lie algebras II"

Known classification results allow us to find the number of fine gradings on matrix algebras and on classical simple Lie algebras over an algebraically closed field (assuming that characteristic is not 2 in Lie case). The computation is easy for matrix algebras and especially for simple Lie algebras of Series B, but involves counting orbits of certain finite groups in the case of Series A, C and D. We determine the exact number of fine gradings on the simple Lie algebras of these series up to rank 100 as well as the asymptotic behaviour of the average number of fine gradings for large rank. This is joint work with Nicholas Parsons and Sergey Sadov.

*HH-3017 1:00-2:00 p.m.*

**October 31, 2012**

Mikhail Kotchetov (Memorial University) "Counting fine gradings on matrix algebras and on classical simple Lie algebras I"

Known classification results allow us to find the number of fine gradings on matrix algebras and on classical simple Lie algebras over an algebraically closed field (assuming that characteristic is not 2 in Lie case). The computation is easy for matrix algebras and especially for simple Lie algebras of Series B, but involves counting orbits of certain finite groups in the case of Series A, C and D. We determine the exact number of fine gradings on the simple Lie algebras of these series up to rank 100 as well as the asymptotic behaviour of the average number of fine gradings for large rank. This is joint work with Nicholas Parsons and Sergey Sadov.

*HH-3017, 1:00 - 2:00 p.m.*

**September ****26, 2012**

Yuri Bahturin (Memorial University) "Group gradings on nilpotent Lie algebras. II"

Abstract: In this talk we are going to show how some basic techniques from the theory of algebraic groups can be used to classify gradings by abelian groups on nilpotent Lie algebras. The presence of such gradings has consequences for the symmetric structures on the related homogeneous spaces.

*HH-3017, 1:00 - 2:00 p.m.*

*September 19, 2012*

Yuri Bahturin (Memorial University)

"Group gradings on nilpotent Lie algebras"

**Abstract: **In this talk we are going to show how some basic techniques from the theory of algebraic groups can be used to classify gradings by abelian groups on nilpotent Lie algebras. The presence of such gradings has consequences for the symmetric structures on the related homogeneous spaces.

*HH-3017, 1:00 - 2:00 p.m.*