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arXiv · 1309.7133

On classification of quantum groups and Belavin-Drinfeld twisted cohomologies

Alexander Stolin·Iulia Pop
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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 $\mathbb{K}=\mathbb{C}((\hbar))$, 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 $o(n)$.

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Alexander Stolin, Iulia Pop. 2013-09-27. On classification of quantum groups and Belavin-Drinfeld twisted cohomologies. https://arxiv.org/abs/1309.7133

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