Hom-bialgebras and comodule Hom-algebras

Abstract

We study Hom-bialgebras and objects admitting coactions by Hom-bialgebras. In particular, we construct a Hom-bialgebra M representing the functor of 2x2-matrices on Hom-associative algebras. Then we construct a Hom-algebra analogue of the affine plane and show that it is a comodule Hom-algebra over M in a suitable sense. It is also shown that the enveloping Hom-associative algebra of a Hom-Lie algebra is naturally a Hom-bialgebra.

20 pages. To appear in the International Electronic Journal of Algebra

References in corpus (12)

• Deformations of Lie Algebras using $\sigma$-derivations
• 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-quantum groups III: Representations and module Hom-algebras
• Hom-Lie admissible Hom-coalgebras and Hom-Hopf algebras
• On Hom type algebras
• Hom-alternative algebras and Hom-Jordan algebras
• On hom-algebras with surjective twisting

Cited by in corpus (26)

• Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras
• Hom-quantum groups I: quasi-triangular Hom-bialgebras
• BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras
• On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
• Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras
• Yetter-Drinfeld modules for Hom-bialgebras
• Ternary q-Virasoro-Witt Hom-Nambu-Lie 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
• Cyclic homology for Hom-associative algebras
• Hom-alternative algebras and Hom-Jordan algebras
• Hom-Algebras and Hom-Coalgebras
• Hom Gel'fand-Dorfman bialgebras and Hom-Lie conformal algebras
• Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras
• Free involutive Hom-semigroups and Hom-associative algebras
• On n-ary Hom-Nambu and Hom-Maltsev algebras
• Universal enveloping algebras and Poincaré-Birkhoff-Witt theorem for involutive Hom-Lie algebras
• On Antipodes Of Hom-Hopf algebras
• Covariant Bimodules Over Monoidal Hom-Hopf Algebras
• Hom-coassociative ternary coalgebras and infinitesimal bialgebras
• Four-angle Hopf modules for Hom-Hopf algebras
• Hom-pre-Malcev and Hom-M-Dendriform algebras
• Super Hom-Gel'fand-Dorfman bialgebras and Hom-Lie conformal superalgebras
• Crossed product Hom-Hopf algebras and lazy 2-cocycle
• Yetter-Drinfeld modules for weak Hom-Hopf algebras