Belavin-Drinfeld cohomologies and introduction to classification of quantum groups
Artikel i vetenskaplig tidskrift, 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.

quantum groups

Belavin-Drinfeld cohomology


Alexander Stolin

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Iulia Pop

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Journal of Physics: Conference Series

1742-6588 (ISSN)

Vol. 563