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

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

2009-06-22

arxiv.org/abs/0906.4128v1

Journal of Physics A 45 (2012) 065203

Physics

Mathematical Physics

21 pages

Scientific paper

10.1088/1751-8113/45/6/065203

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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