• Corpus ID: 115158781

Hom-bialgebras and comodule Hom-algebras

@article{Yau2008HombialgebrasAC,
  title={Hom-bialgebras and comodule Hom-algebras},
  author={Donald Yau},
  journal={arXiv: Rings and Algebras},
  year={2008}
}
  • Donald Yau
  • Published 1 October 2008
  • Mathematics
  • arXiv: Rings and Algebras
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. 
Infinitesimal Hom-bialgebras and Hom-Lie bialgebras
We study the Hom-type generalization of infinitesimal bialgebras, called infinitesimal Hom-bialgebras. In particular, we consider infinitesimal Hom-bialgebras arising from quivers, the sub-classes of
Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
The aim of this paper is to give a survey of nonassociative Hom-algebra and Hom-superalgebra structures. The main feature of these algebras is that the identities defining the structures are twisted
2-Hom-Associative Bialgebras and Hom-Left Symmetric Dialgebras
From the definition and properties of unital hom-associative algebras, and the use of the Kaplansky's constructions, we develop new algebraic structures called 2-hom-associative bialgebras,
SOME RESULTS ABOUT HOM-COMODULE ALGEBRAS WITH HOM-HOPF MODULE STRUCTURE
The main subject of this paper is Hom-comodule algebras with Hom-Hopf module structure. First, we give the factorization of a class of Hom- bialgebras, which is not only Hom-module coalgebras but
Gerstenhaber–Schack cohomology for Hom-bialgebras and deformations
ABSTRACT Hom-bialgebras and Hom-Hopf algebras are generalizations of bialgebra and Hopf algebra structures, where associativity and coassociativity conditions are twisted by a homomorphism. The
Hom-algebras and Hom-coalgebras
The aim of this paper is to develop the theory of Hom-coalgebras and related structures. After reviewing some key constructions and examples of quasi-deformations of Lie algebras involving twisted
On Twisted Smash Products of Monoidal Hom–Hopf Algebras
Let (H, α) be a monoidal Hom-Hopf algebra and (A, β) be an (H, α)-Hom-bimodule algebra. In this article, we first introduce the notion of a twisted Hom-smash product A☆H and then find some sufficient
Crossed products of Hom-Hopf algebras
Let (H, α) be a Hom-Hopf algebra and (A, β) be a Hom-algebra. In this paper we will construct the Hom-crossed product (A#σH, β⊗α), and prove that the extension A ⊆ A#σH is actually a Hom-type cleft
On Hom-type algebras
Hom-algebras are generalizations of algebras obtained using a twisting by a linear map. But there is a priori a freedom on where to twist.We enumerate here all the possible choices in the Lie and
Variety of Hom-Sabinin Algebras and Related Algebra Subclasses
The purpose of this paper is to study Sabinin algebras of Hom-type. It is shown that Lie, Malcev, Bol and other algebras of Hom-type are naturally Sabinin algebras of Hom-type. To this end, we
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Hom-algebras are generalizations of algebras obtained using a twisting by a linear map. But there is a priori a freedom on where to twist.We enumerate here all the possible choices in the Lie and
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