On classification of quantum groups and Belavin-Drinfeld twisted cohomologies

Abstract

The present article is a continuation of QA/1303.4046, where we discussed the classification of quantum groups with quasi-classical limit $\mathfrak{g}$ and introduced a theory of Belavin-Drinfeld cohomology associated to any non-skewsymmetric $r$-matrix. Depending on the form of the corresponding double, there exists a one-to-one correspondence between gauge equivalence classes of Lie bialgebra structures on $\mathfrak{g}{\otimes }_{\mathbb{C}}\mathbb{K}$, where $\mathbb{K}=\mathbb{C}((\hslash ))$, and untwisted or twisted cohomology classes. In the present paper we investigate twisted cohomologies for $sl(n)$ associated to generalized Cremmer-Gervais $r$-matrices, and twisted cohomologies for $o(n)$.

The paper has been withdrawn because these results have been improved and are now contained in a more comprehensive paper (math. QA 1502.00403v1) with a different title and more authors

References in corpus (1)

• On Some Lie Bialgebra Structures on Polynomial Algebras and their Quantization