News

Seminario: “Nichols algebras of finite Gelfand-Kirillov dimension over abelian groups”

Mercoledì 23 Novembre 2016, ore 14:30 - Aula 2AB45 - Nicolas Andruskiewitsch

ARGOMENTI: Seminari

Mercoledì 23 Novembre 2016 alle ore 14:30 in Aula 2AB45, Nicolas Andruskiewitsch (Cordoba) terrà un seminario dal titolo “Nichols algebras of finite Gelfand-Kirillov dimension over abelian groups”.

Abstract
In algebraic geometry, there is a topological dimension that can be computed algebraically by means of the Krull dimension. The best analogue in noncommutative geometry is the Gelfand-Kirillov dimension. Thus, Hopf algebras with finite GK-dimension are the noncommutative (or quantum) version of (algebras of rational functions on) algebraic groups. There is a recent activity on the classification of Hopf algebras with finite GK-dimension, see [3]. By the lifting method of Schneider and the speaker, the first unavoidable step is the classification of Nichols algebras with finite GK-dimension.
The talk will be an introduction to this classification and an overview of the classification of Nichols algebras with finite GK-dimension over abelian groups, including numerous new examples.

References:
[1] N. Andruskiewitsch, I. Angiono and I. Heckenberger. On finite GK-dimensional Nichols algebras over abelian groups, arXiv:1606.02521 [arxiv.org].
[2] N. Andruskiewitsch, I. Angiono and I. Heckenberger. Liftings of Jordan and super Jordan planes. arXiv:1512.09271 [arxiv.org].
[3] Report on the workshop Nichols Algebras and Their Interactions with Lie Theory, Hopf Algebras and Tensor
Categories. http://www.birs.ca/workshops/2015/15w5053/report15w5053.pdf [www.birs.ca]