Associative triples and the Yang-Baxter equation

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 i...

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Bibliographic Details
Published in:Israel journal of mathematics 2004-01, Vol.139 (1), p.11-28
Main Author: Mudrov, A. I.
Format: Article
Language:English
Subjects:
Mathematical analysis
Mathematics
Matrices (mathematics)
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Summary: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 theAn-type Belavin-Drinfel’d triples are derived in this way.
ISSN:0021-2172
1565-8511
DOI:10.1007/BF02787540