Classification of Quantum Groups and Belavin–Drinfeld Cohomologies

  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},
  • Boris Kadets, E. Karolinsky, +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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