On the classification of Quantum groups

Host Institution:

La Trobe University

Title of Seminar:

On the classification of Quantum groups

Speaker's Name:

Professor Alexander Stolin

Speaker's Institution:

University of Gothenburg, Sweden

Time and Date:

Friday 15 November, 2.00pm (AEDT)

Seminar Abstract:

We will explain an approach to classification of certain quantum groups. Let g be a complex simple Lie algebra. A quantum group is a Hopf algebra over C[[h]], which has g as its classical limit. To obtain it we, roughly speaking, set h=0. More precisely, being a classical limit of a Hopf algebra, g becomes a Lie bialgebra. It is well-known that simple Lie algebras are classified by means of the so-called Dynkin diagrams. In 1982, Belavin and Drinfeld classified the corresponding Lie bialgebras by means of the Belavin-Drinfeld triples, which can be described as two isomorphic subdiagrams of the Dynkin diagram of g (they are called triples because the isomorphism between the subdiagrams matters). In order to classify the corresponding quantum groups we introduced further combinatorial data, which we called Belavin-Drinfeld cohomologies. There are two types of the BD-cohomologies, namely nontwisted and twisted versions.In my talk, I will explain how to describe BD-cohomologies for special linear and orthogonal algebras. No prior knowledge except for the standard facts about simple Lie algebras is needed.

This is a joint work Iulia Pop (Chalmers University of Technology, Sweden).

 

 

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