Quantization of certain skew-symmetric solutions of the classical Yang-Baxter equation

Details Quantization of certain skew-symmetric solutions of the classical Yang-Baxter equation Quantization of certain skew-symmetric solutions of the classical Yang-Baxter equation

2000-03-10

arxiv.org/abs/math/0003066v2

Mathematics

Quantum Algebra

Some significant errors and typos corrected

Scientific paper

An explicit quantization is given of certain skew-symmetric solutions of the classical Yang-Baxter, yielding a family of $R$-matrices which generalize to higher dimensions the Jordanian $R$-matrices. Three different approaches to their construction are given: as twists of degenerations of the Shibukawa-Ueno Yang-Baxter operators on meromorphic functions; as boundary solutions of the quantum Yang-Baxter equation; via a vertex-IRF transformation from solutions to the dynamical Yang-Baxter equation.

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