## Special day on Lie groups: September 4, 2014

### At the occasion of the thesis defense of Dana Balibanu

Title thesis: Convexity theorems for symmetric spaces and representations of n-Lie algebras. Two studies in Lie theory.
Date thesis defense: Wednesday, September 3, 2014
Time: 12:45

### Thursday, September 4

9:50 - 10:10: coffee

10:10 - 10:55: J. Hilgert (Paderborn): Vinberg's enveloping semigroup and its symplectic analog

11:05 - 11:50: A. Dzhumadildaev (Almaty, Kazakhstan): N-commutators, norms and identities on Weyl algebras

12:00 - 12:45: J. Stokman: (University of Amsterdam): Connection problems in the context of quantum integrable systems

Lunch

Location: Hans Freudenthal (Math) building, room 611.

### Abstracts:

• J. Hilgert:
Vinberg constructed for any complex semisimple algebraic group G a semigroup which is a flat family of semigroups whose unit groups have G as a commutator group. This family can be used to define contractions of G-varieties. In this talk we will explain some relations with recent work of Harada and Kaveh on toric degenerations and integrable systems.

The Weyl algebra $A_n$ is an algebra of differential operators on the polynomials algebra C[x_1, …. ,x_n]. We prove that the subspace of $A_1$ with differential degree $p$ admits a $2p$-commutator. We construct a scalar product and norm on $A_1.$ We show that an analog of the Amitsur-Levitzki identity for differential operators of first order pass only for $n\le 3.$
1. { $2p$-Commutator on differential operators of order $p$}, Letters Math. Phys., {\bf 104}(2014), No.7, pp 849-869