# Classification of Quantum Groups and Belavin–Drinfeld Cohomologies

@article{Kadets2013ClassificationOQ,
title={Classification of Quantum Groups and Belavin–Drinfeld Cohomologies},
author={Boris Kadets and E. Karolinsky and I. Pop and A. Stolin},
journal={Communications in Mathematical Physics},
year={2013},
volume={344},
pages={1-24}
}
• Boris Kadets, +1 author A. Stolin
• Published 2013
• Mathematics
• Communications in Mathematical Physics
• In the present article we discuss the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra $${\mathfrak{g}}$$g. This problem is reduced to the classification of all Lie bialgebra structures on $${\mathfrak{g}(\mathbb{K})}$$g(K), where $${\mathbb{K}=\mathbb{C}((\hbar))}$$K=C((ħ)). The associated classical double is of the form $${\mathfrak{g}(\mathbb{K})\otimes_{\mathbb{K}} A}$$g(K)⊗KA, where A is one of the following: $${\mathbb{K}[\varepsilon]}$$K… CONTINUE READING
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