Spectral-parameter dependent Yang-Baxter operators and Yang-Baxter systems from algebra structures

Details Spectral-parameter dependent Yang-Baxter operators and Yang-Baxter systems from algebra structures Spectral-parameter dependent Yang-Baxter operators and Yang-Baxter systems from algebra structures

2006-07-27

arxiv.org/abs/math/0607710v1

Comm. Algebra 34 (2006) 2713-2726

Mathematics

Quantum Algebra

13 pages, LaTeX

Scientific paper

For any algebra two families of coloured Yang-Baxter operators are constructed, thus producing solutions to the two-parameter quantum Yang-Baxter equation. An open problem about a system of functional equations is stated. The matrix forms of these operators for two and three dimensional algebras are computed. A FRT bialgebra for one of these families is presented. Solutions for the one-parameter quantum Yang-Baxter equation are derived and a Yang-Baxter system constructed.

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