Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry
arXiv:0907.1880
Abstract
A class of non-associative and non-coassociative generalizations of cobraided bialgebras, called cobraided Hom-bialgebras, is introduced. The non-(co)associativity in a cobraided Hom-bialgebra is controlled by a twisting map. Several methods for constructing cobraided Hom-bialgebras are given. In particular, Hom-type generalizations of FRT quantum groups, including quantum matrices and related quantum groups, are obtained. Each cobraided Hom-bialgebra comes with solutions of the operator quantum Hom-Yang-Baxter equations, which are twisted analogues of the operator form of the quantum Yang-Baxter equation. Solutions of the Hom-Yang-Baxter equation can be obtained from comodules of suitable cobraided Hom-bialgebras. Hom-type generalizations of the usual quantum matrices coactions on the quantum planes give rise to non-associative and non-coassociative analogues of quantum geometry.
38 pages
References in corpus (8)
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- Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
- Module Hom-algebras
- The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
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Cited by in corpus (7)
- On unitality conditions for Hom-associative algebras
- Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
- Hom-alternative algebras and Hom-Jordan algebras
- Infinitesimal Hom-bialgebras and Hom-Lie bialgebras
- Hom-power associative algebras
- Construtions and bimodules of BiHom-alternative and BiHom-Jordan algebras
- Deforming algebras with anti-involution via twisted associativity