期刊
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
卷 9, 期 4, 页码 553-589出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219498810004117
关键词
Hom-Lie algebra; Hom-associative algebra; Hom-coalgebra; Hom-bialgebra; Hom-Hopf algebra; Hom-Lie admissible Hom-coalgebra
资金
- Crafoord Foundation
- Royal Swedish Academy of Sciences
- Swedish Research Council
- SIDA Foundation and Swedish Research Council
- Swedish Foundation of International Cooperation in Research and High Education (STINT)
- Royal Physiographic Society in Lund, University of Mulhouse and Lund University
- European network Liegrits
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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