Belavin-Drinfeld cohomologies and introduction to classification of quantum groups
Paper in proceeding, 2014

In the present article we discuss the classification of quantum groups whose quasiclassical limit is a given simple complex Lie algebra g. This problem reduces to the classification of all Lie bialgebra structures on g(K), where K = C((hbar)). The associated classical double is of the form g(K)⊗K A, where A is one of the following: K[ε], where ε2 =0, K ⊕ K or K[j], where j2 = hbar. The first case relates to quasi-Frobenius Lie algebras. In the second and third cases we introduce a theory of Belavin-Drinfeld cohomology associated to any non-skewsymmetric r-matrix from the Belavin-Drinfeld list [1]. We prove a one-to-one correspondence between gauge equivalence classes of Lie bialgebra structures on g(K) and cohomology classes (in case II) and twisted cohomology classes (in case III) associated to any non-skewsymmetric r-matrix.

Belavin-Drinfeld cohomology

quantum groups


Alexander Stolin

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Iulia Pop

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Journal of Physics: Conference Series

17426588 (ISSN) 17426596 (eISSN)

Vol. 563 1 012030

22nd International Conference on Integrable Systems and Quantum Symmetries, ISQS 2014
Prag, Czech Republic,

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Physical Sciences



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