Module Hom-algebras

Abstract

We study a twisted version of module algebras called module Hom-algebras. It is shown that module algebras deform into module Hom-algebras via endomorphisms. As an example, we construct certain q-deformations of the usual sl(2)-action on the affine plane.

10 pages

References in corpus (5)

• Deformations of Lie Algebras using $\sigma$-derivations
• Hom-algebras and homology
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• Hom-Algebras and Hom-Coalgebras
• The L_\infty-deformation complex of diagrams of algebras

Cited by in corpus (20)

• Hom-algebras and homology
• Hom-bialgebras and comodule Hom-algebras
• Hom-quantum groups I: quasi-triangular Hom-bialgebras
• BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras
• The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
• Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry
• Hom-quantum groups III: Representations and module Hom-algebras
• BiHom-Lie superalgebra structures
• Transposed Hom-Poisson and Hom-pre-Lie Poisson algebras and bialgebras
• Construtions and bimodules of BiHom-alternative and BiHom-Jordan algebras
• Bimodules over Hom-Jordan and Hom-alternative algebras
• Structures and bimodules of simple Hom-alternative algebras
• Hom-Tensor Categories and the Hom-Yang-Baxter Equation
• Hom-pre-Malcev and Hom-M-Dendriform algebras
• The Hom-Long dimodule category and nonlinear equations
• Cobraided Smash Product Hom-Hopf Algebras
• Color Hom-Akivis algebras, Color Hom-Leibniz algebras and Modules over Color Hom-Leibniz algebras
• Hom-Lie-Hopf algebras
• The Drinfel'd Double versus the Heisenberg Double for Hom-Hopf Algebras
• Four-angle Hopf modules for Hom-Hopf algebras