On unified Hom–Yetter–Drinfeld categories
| Autor: | Tianshui Ma, Haiyan Yang, Linlin Liu, Quanguo Chen |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Degree (graph theory)
Mathematics::Rings and Algebras 010102 general mathematics General Physics and Astronomy 01 natural sciences Combinatorics Bracket (mathematics) Mathematics::Quantum Algebra Mathematics::Category Theory Product (mathematics) 0103 physical sciences Lie algebra Bijection 010307 mathematical physics Geometry and Topology 0101 mathematics Symmetry (geometry) Algebra over a field Commutative property Mathematical Physics Mathematics |
| Zdroj: | Journal of Geometry and Physics. 144:81-107 |
| ISSN: | 0393-0440 |
| DOI: | 10.1016/j.geomphys.2019.05.015 |
| Popis: | In this paper, we discuss properties of the unified Hom–Yetter–Drinfeld categories H H HYD ( l ) , where ( H , β ) is a Hom–Hopf algebra with bijective antipode S and l ∈ Z (the set of integers). On one hand, we prove the following results about the symmetry and pseudosymmetry of H H HYD ( l ) : If H H HYD ( l ) is symmetric then H is trivial; H H HYD ( l ) is pseudosymmetric if and only if ( H , α ) is commutative and cocommutative; The relations between u-condition of Hom-type and the symmetry of H H HYD ( l ) ; The (co)representation category of (co)triangular Hom–Hopf algebra is symmetric. On the other hand, we focus on the category H H HYD ( 0 ) . We introduce the notion of (0 degree) unified H -Lie algebra, then show that a Hom-algebra ( A , α ) satisfying additional conditions gives rise to (0 degree) unified H -Lie algebra with suitable bracket product. And if ( A , α ) also has two Hom-subalgebras U and X which are ( H , β ) -commutative such that A = U + X , then we prove that [ A , A ] [ A , A ] = 0 . |
| Databáze: | OpenAIRE |
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