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Hom-Algebras And Hom-Coalgebras

Makhlouf, Abdenacer and Silvestrov, Sergei LU (2010) In Journal of Algebra and Its Applications 9(4). p.553-589
Abstract
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 derivations and giving rise to the class of quasi-Lie algebras incorporating Hom-Lie algebras, we describe the notion and some properties of Hom-algebras and provide examples. We introduce Hom-coalgebra structures, leading to the notions of Hom-bialgebra and Hom-Hopf algebras, and prove some fundamental properties and give examples. Finally, we define the concept of Hom-Lie admissible Hom-coalgebra and provide their classification based on subgroups of the symmetric group.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Hom-Lie algebra, Hom-coalgebra, Hom-bialgebra, Hom-Lie admissible Hom-coalgebra, Hom-Hopf algebra, Hom-associative algebra
in
Journal of Algebra and Its Applications
volume
9
issue
4
pages
553 - 589
publisher
World Scientific
external identifiers
  • wos:000281665700004
  • scopus:77953351963
ISSN
0219-4988
DOI
10.1142/S0219498810004117
language
English
LU publication?
yes
id
e109bca7-7d34-4e16-bd5f-a3d6bb304651 (old id 1697668)
date added to LUP
2010-10-22 16:20:22
date last changed
2018-06-24 03:31:37
@article{e109bca7-7d34-4e16-bd5f-a3d6bb304651,
  abstract     = {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 derivations and giving rise to the class of quasi-Lie algebras incorporating Hom-Lie algebras, we describe the notion and some properties of Hom-algebras and provide examples. We introduce Hom-coalgebra structures, leading to the notions of Hom-bialgebra and Hom-Hopf algebras, and prove some fundamental properties and give examples. Finally, we define the concept of Hom-Lie admissible Hom-coalgebra and provide their classification based on subgroups of the symmetric group.},
  author       = {Makhlouf, Abdenacer and Silvestrov, Sergei},
  issn         = {0219-4988},
  keyword      = {Hom-Lie algebra,Hom-coalgebra,Hom-bialgebra,Hom-Lie admissible Hom-coalgebra,Hom-Hopf algebra,Hom-associative algebra},
  language     = {eng},
  number       = {4},
  pages        = {553--589},
  publisher    = {World Scientific},
  series       = {Journal of Algebra and Its Applications},
  title        = {Hom-Algebras And Hom-Coalgebras},
  url          = {http://dx.doi.org/10.1142/S0219498810004117},
  volume       = {9},
  year         = {2010},
}