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PreprintCC BY 4.0arXiv

BiHom-L-R-smash biproduct and BiHom-Yetter-Drinfel'd-Long category

  • Dongdong Yan
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Abstract

In this article, we first introduce the notion of BiHom-L-R-binomm,n,p,qs,t,u,v-smash biproduct over a BiHom-Hopf algebra, denoted by Dnatural H, where m,n,p,q,s,t,u,v∈ ℤ, and give the sufficient condition for Dnatural H to be a BiHom-bialgebra. Furthermore, we describe the concept of BiHom-binomm,n,p,qs,t,u,v-Yetter-Drinfel'd-Long bimodule via BiHom-L-R-binomm,n,p,qs,t,u,v-smash biproduct bialgebra, and prove that the category ℒℛ(H)(m,n,p,q) of BiHom-binomm,n,p,qs,t,u,v-Yetter-Drinfel'd-Long bimodule is a strict braided monoidal category. Finally, for a finite-dimensional BiHom-Hopf algebra H, ℒℛ(H)binomm,n,p,qs,t,u,v is isomorphic to the BiHom-binoms,tp,q-Yetter-Drinfel'd category H⊗ H*H⊗ H*𝒴𝒟binoms,tp,q as braided monoidal categories.

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Cite

BibTeXRIS
BibTeX
@misc{yan2026bihomlrsmash,
  title = {{BiHom-L-R-smash biproduct and BiHom-Yetter-Drinfel'd-Long category}},
  author = {Dongdong Yan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.26510},
  eprint = {2607.26510},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.26510},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - BiHom-L-R-smash biproduct and BiHom-Yetter-Drinfel'd-Long category
AU  - Dongdong Yan
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2607.26510
UR  - https://arxiv.org/abs/2607.26510
AB  - In this article, we first introduce the notion of BiHom-L-R-binomm,n,p,qs,t,u,v-smash biproduct over a BiHom-Hopf algebra, denoted by Dnatural H, where m,n,p,q,s,t,u,v∈ ℤ, and give the sufficient condition for Dnatural H to be a BiHom-bialgebra. Furthermore, we describe the concept of BiHom-binomm,n,p,qs,t,u,v-Yetter-Drinfel'd-Long bimodule via BiHom-L-R-binomm,n,p,qs,t,u,v-smash biproduct bialgebra, and prove that the category ℒℛ(H)(m,n,p,q) of BiHom-binomm,n,p,qs,t,u,v-Yetter-Drinfel'd-Long bimodule is a strict braided monoidal category. Finally, for a finite-dimensional BiHom-Hopf algebra H, ℒℛ(H)binomm,n,p,qs,t,u,v is isomorphic to the BiHom-binoms,tp,q-Yetter-Drinfel'd category _H⊗ H^*^H⊗ H^*𝒴𝒟binoms,tp,q as braided monoidal categories.
ER  -