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, 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
    11 Citations

    Tables from this paper

    Classification of Quantum Groups via Galois Cohomology
    • 2
    • PDF
    Q A ] 2 8 A ug 2 01 9 Classification of Quantum Groups via Galois Cohomology
    Lie Bialgebras, Fields of Cohomological Dimension at Most 2 and Hilbert's Seventeenth Problem
    • 1
    • PDF

    References

    SHOWING 1-10 OF 15 REFERENCES
    Classification of Lie bialgebras over current algebras
    • 21
    • PDF
    Lectures on Quantum Groups
    • 350
    • PDF
    Quantization of Lie bialgebras, I
    • 197
    • PDF
    Quantum Groups
    • 2,492
    • PDF
    Quantum Groups
    • 4,281
    Quantization of Lie bialgebras, II
    • 262
    • PDF
    Triangle Equations and Simple Lie Algebras
    • 129
    • Highly Influential