Parametric representations of BiHom-Hopf algebras

Xiaohui Zhang; Wei Wang; Juzhen Chen

Czechoslovak Mathematical Journal (2024)

  • Issue: 1, page 45-86
  • ISSN: 0011-4642

Abstract

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The main purpose of the present paper is to study representations of BiHom-Hopf algebras. We first introduce the notion of BiHom-Hopf algebras, and then discuss BiHom-type modules, Yetter-Dinfeld modules and Drinfeld doubles with parameters. We get some new n -monoidal categories via the category of BiHom-(co)modules and the category of BiHom-Yetter-Drinfeld modules. Finally, we obtain a center construction type theorem on BiHom-Hopf algebras.

How to cite

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Zhang, Xiaohui, Wang, Wei, and Chen, Juzhen. "Parametric representations of BiHom-Hopf algebras." Czechoslovak Mathematical Journal (2024): 45-86. <http://eudml.org/doc/299231>.

@article{Zhang2024,
abstract = {The main purpose of the present paper is to study representations of BiHom-Hopf algebras. We first introduce the notion of BiHom-Hopf algebras, and then discuss BiHom-type modules, Yetter-Dinfeld modules and Drinfeld doubles with parameters. We get some new $n$-monoidal categories via the category of BiHom-(co)modules and the category of BiHom-Yetter-Drinfeld modules. Finally, we obtain a center construction type theorem on BiHom-Hopf algebras.},
author = {Zhang, Xiaohui, Wang, Wei, Chen, Juzhen},
journal = {Czechoslovak Mathematical Journal},
keywords = {BiHom-Hopf algebra; BiHom-Yang-Baxter equation; $n$-monoidal category; Drinfeld double},
language = {eng},
number = {1},
pages = {45-86},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Parametric representations of BiHom-Hopf algebras},
url = {http://eudml.org/doc/299231},
year = {2024},
}

TY - JOUR
AU - Zhang, Xiaohui
AU - Wang, Wei
AU - Chen, Juzhen
TI - Parametric representations of BiHom-Hopf algebras
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 45
EP - 86
AB - The main purpose of the present paper is to study representations of BiHom-Hopf algebras. We first introduce the notion of BiHom-Hopf algebras, and then discuss BiHom-type modules, Yetter-Dinfeld modules and Drinfeld doubles with parameters. We get some new $n$-monoidal categories via the category of BiHom-(co)modules and the category of BiHom-Yetter-Drinfeld modules. Finally, we obtain a center construction type theorem on BiHom-Hopf algebras.
LA - eng
KW - BiHom-Hopf algebra; BiHom-Yang-Baxter equation; $n$-monoidal category; Drinfeld double
UR - http://eudml.org/doc/299231
ER -

References

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