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arXiv · 0903.1466

Degenerate Sklyanin Algebras

Andrey Smirnov
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Abstract

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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Andrey Smirnov. 2009-03-08. Degenerate Sklyanin Algebras. https://doi.org/10.2478/s11534-009-0142-5

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