Hom-Algebras And Hom-Coalgebras
(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:
https://lup.lub.lu.se/record/1697668
- author
- Makhlouf, Abdenacer and Silvestrov, Sergei LU
- organization
- publishing date
- 2010
- 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}}, }