Classification of Quantum Groups and Belavin–Drinfeld Cohomologies

Boris Kadets, Eugene Karolinsky, Iulia Pop*, Alexander Stolin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

In the present article we discuss the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra g. This problem is reduced to the classification of all Lie bialgebra structures on g(K) , where K= C((ħ)). The associated classical double is of the form g(K) ⊗ KA, where A is one of the following: K[ ε] , where ε2= 0 , K⊕ K or K[ j] , where j2= ħ. The first case is related 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 on the Belavin–Drinfeld list (Belavin and Drinfeld in Soviet Sci Rev Sect C: Math Phys Rev 4:93–165, 1984). 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.

Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalCommunications in Mathematical Physics
Volume344
Issue number1
DOIs
StatePublished - 1 May 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.

Fingerprint

Dive into the research topics of 'Classification of Quantum Groups and Belavin–Drinfeld Cohomologies'. Together they form a unique fingerprint.

Cite this