Hom-quantum groups III: Representations and module Hom-algebras
arXiv:0911.5402
Abstract
We study Hom-quantum groups, their representations, and module Hom-algebras. Two Twisting Principles for Hom-type algebras are formulated, and construction results are proved following these Twisting Principles. Examples include Hom-quantum n-spaces, Hom-quantum enveloping algebras of Kac-Moody algebras, Hom-Verma modules, and Hom-type analogs of U_q(sl_2)-module-algebra structures on the quantum planes.
35 pages
References in corpus (10)
- Hom-algebras and homology
- Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
- Module Hom-algebras
- The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
- Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry
- On unitality conditions for Hom-associative algebras
- Hom-alternative algebras and Hom-Jordan algebras
- On Hom type algebras
- Hom-Algebras and Hom-Coalgebras
- On hom-algebras with surjective twisting
Cited by in corpus (13)
- BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras
- On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
- Yetter-Drinfeld modules for Hom-bialgebras
- Hom-Maltsev, Hom-alternative, and Hom-Jordan algebras
- Infinitesimal Hom-bialgebras and Hom-Lie bialgebras
- On n-ary Hom-Nambu and Hom-Maltsev algebras
- Hom-power associative algebras
- Hom-post-Lie modules, O-operators and some functors on Hom-algebras
- Covariant Bimodules Over Monoidal Hom-Hopf Algebras
- Hom-Tensor Categories and the Hom-Yang-Baxter Equation
- Cobraided Smash Product Hom-Hopf Algebras
- Four-angle Hopf modules for Hom-Hopf algebras
- Deforming algebras with anti-involution via twisted associativity