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Belavin-Drinfeld cohomologies and introduction to classification of quantum groups

Alexander Stolin (Institutionen för matematiska vetenskaper, matematik) ; Iulia Pop (Institutionen för matematiska vetenskaper, matematik)
Journal of Physics, Conference Series (1742-6588). Vol. 563 (2014), 1,
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: quantum groups, Belavin-Drinfeld cohomology

Denna post skapades 2015-10-29. Senast ändrad 2015-11-04.
CPL Pubid: 225014


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