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Solutions for the constant quantum Yang-Baxter equation from Lie (super)algebras

  • Author(s): Tanasa, A.
  • Ballesteros, A.
  • Herranz, F. J.
  • et al.

Published Web Location

https://arxiv.org/pdf/0704.3334.pdf
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Abstract

We present a systematic procedure to obtain singular solutions of the constant quantum Yang-Baxter equation in arbitrary dimension. This approach, inspired in the Lie (super)algebra structure, is explicitly applied to the particular case of (graded) contractions of the orthogonal real algebra ${\mathfrak{so}}(N+1)$. In this way we show that "classical" contraction parameters which appear in the commutation relations of the contracted Lie algebras, become quantum deformation parameters, arising as entries of the resulting quantum $R$-matrices.

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