Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

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.
Please use this url to cite or link to this publication:
author
and
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 Publishing
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
2016-04-01 10:58:57
date last changed
2022-02-25 07:31:10
@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}},
  keywords     = {{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 Publishing}},
  series       = {{Journal of Algebra and Its Applications}},
  title        = {{Hom-Algebras And Hom-Coalgebras}},
  url          = {{http://dx.doi.org/10.1142/S0219498810004117}},
  doi          = {{10.1142/S0219498810004117}},
  volume       = {{9}},
  year         = {{2010}},
}