Classification of quantum groups and Belavin--Drinfeld cohomologies for orthogonal and symplectic Lie algebras

Abstract

In this paper we continue to study Belavin-Drinfeld cohomology introduced in arXiv:1303.4046 [math.QA] and related to the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra. Here we compute Belavin-Drinfeld cohomology for all non-skewsymmetric $r$-matrices from the Belavin-Drinfeld list for simple Lie algebras of type $B$, $C$, and $D$.

17 pages

Cited by in corpus (3)

• Classification of Quantum Groups via Galois cohomology
• Quantum groups: from Kulish-Reshetikhin discovery to classification
• Belavin-Drinfeld quantum groups and Lie bialgebras: Galois cohomology considerations