| Title | Hom-Algebras And Hom-Coalgebras |
| Authors | Abdenacer Makhlouf, Sergei Silvestrov |
| Alternative Location | http://dx.doi.org/10.1142/S..., Restricted Access |
| Publication | Journal Of Algebra And Its Applications |
| Year | 2010 |
| Volume | 9 |
| Issue | 4 |
| Pages | 553 - 589 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | World Scientific Publ Co Pte Ltd |
| Abstract English | 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. |
| Keywords | Hom-Lie algebra, Hom-coalgebra, Hom-bialgebra, Hom-Lie admissible Hom-coalgebra, Hom-Hopf algebra, Hom-associative algebra, |
| ISBN/ISSN/Other | ISSN: 0219-4988 |
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