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arXiv · 0906.4128

Hom-quantum groups I: quasi-triangular Hom-bialgebras

Donald Yau
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Abstract

We introduce a Hom-type generalization of quantum groups, called quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative analogues of Drinfel'd's quasi-triangular bialgebras, in which the non-(co)associativity is controlled by a twisting map. A family of quasi-triangular Hom-bialgebras can be constructed from any quasi-triangular bialgebra, such as Drinfel'd's quantum enveloping algebras. Each quasi-triangular Hom-bialgebra comes with a solution of the quantum Hom-Yang-Baxter equation, which is a non-associative version of the quantum Yang-Baxter equation. Solutions of the Hom-Yang-Baxter equation can be obtained from modules of suitable quasi-triangular Hom-bialgebras.

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BibTeXRIS

Donald Yau. 2009-06-22. Hom-quantum groups I: quasi-triangular Hom-bialgebras. https://doi.org/10.1088/1751-8113/45/6/065203

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