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

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

2007-04-25

arxiv.org/abs/0704.3334v1

J.Geom.Symm.Phys.10:83-91,2007

Mathematics

Quantum Algebra

8 pages

Scientific paper

10.1063/1.1900386

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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