Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry

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.

arXiv comment38 pages

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Cited by in corpus (17)

• Hom-bialgebras and comodule Hom-algebras
• Hom-quantum groups I: quasi-triangular Hom-bialgebras
• On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
• Yetter-Drinfeld modules for Hom-bialgebras
• On unitality conditions for Hom-associative algebras
• Hom-quantum groups III: Representations and module Hom-algebras
• Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
• Hom-Maltsev, Hom-alternative, and Hom-Jordan algebras
• Hom-alternative algebras and Hom-Jordan algebras
• Infinitesimal Hom-bialgebras and Hom-Lie bialgebras
• On n-ary Hom-Nambu and Hom-Maltsev algebras
• Hom-power associative algebras
• Construtions and bimodules of BiHom-alternative and BiHom-Jordan algebras
• On Antipodes Of Hom-Hopf algebras
• Covariant Bimodules Over Monoidal Hom-Hopf Algebras
• Deforming algebras with anti-involution via twisted associativity
• Cobraided Smash Product Hom-Hopf Algebras