Yetter-Drinfeld modules for Hom-bialgebras
By Abdenacer Makhlouf, Florin Panaite. 2013
82 citations recorded by the source corpus.
The aim of this paper is to define and study Yetter-Drinfeld modules over Hom-bialgebras, a generalized version of bialgebras obtained by modifying the algebra and coalgebra structures by a homomorphism. Yetter-Drinfeld modules over a Hom-bialgebra with bijective structure map provide solutions of the Hom-Yang-Baxter equation. The category $_H^H{\mathcal YD}$ of Yetter-Drinfeld modules with bijective structure maps over a Hom-bialgebra H with bijective structure map can be organized, in two different ways, as a quasi-braided pre-tensor category. If H is quasitriangular (respectively coquasitriangular) the first (respectively second) quasi-braided pre-tensor category $_H^H{\mathcal YD}$ contains, as a quasi-braided pre-tensor subcategory, the category of modules (respectively comodules) with bijective structure maps over H.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/453baecee1c056826e1365993c1a4f4fa427032d
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In Algebra and Number Theory
- Florin Panaite
- G. Graziani
- Claudia Menini
- Abdenacer Makhlouf
- Donald Yau
- Y. Sheng
- Sergei Silvestrov
- F. Ammar
In Geometry and Topology
- Florin Panaite
- G. Graziani
- Claudia Menini
- Abdenacer Makhlouf
- Donald Yau
- Michael E. Hoffman
- Y. Sheng
- F. Ammar
In Mathematical Physics
Citations in the corpus
- BiHom-associative algebras, BiHom-Lie algebras and BiHom-bialgebras (2015, background): “In the last years, many concepts and properties from classical algebraic theories have been extended to the framework of Hom-structures, see for instance [2, 3, 7, 8, 11, 16, 20, 22, 25, 26, 27, 31, 30].”