Degenerate Sklyanin Algebras

Details Degenerate Sklyanin Algebras Degenerate Sklyanin Algebras

2009-03-08

arxiv.org/abs/0903.1466v1

Physics

Mathematical Physics

12 pages

Scientific paper

New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for $sl(2,\mathbb{C})$. These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The $sl(N,\mathbb{C})$-case is discussed.

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