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 wellknown that simple Lie algebras are classified by means of the socalled Dynkin diagrams. In 1982, Belavin and Drinfeld classified the corresponding Lie bialgebras by means of the BelavinDrinfeld 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 BelavinDrinfeld cohomologies. There are two types of the BDcohomologies, namely nontwisted and twisted versions.In my talk, I will explain how to describe BDcohomologies 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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