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Associative triples and the Yang-Baxter equation

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Abstract

We introduce triples of associative algebras as a tool for building solutions to the Yang-Baxter equation. It turns out that the class of R-matrices thus obtained is related to a Hecke-like condition, which is formulated in the framework of associative algebras with non-degenerate symmetric cyclic inner product. R-matrices for a subclass of theA n-type Belavin-Drinfel’d triples are derived in this way.

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Authors and Affiliations

  1. Department of Mathematics, Bar Ilan University, 52900, Ramat Gan, Israel

    A. I. Mudrov

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  1. A. I. Mudrov
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Mudrov, A.I. Associative triples and the Yang-Baxter equation. Isr. J. Math. 139, 11–28 (2004). https://doi.org/10.1007/BF02787540

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  • DOI: https://doi.org/10.1007/BF02787540

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