# A construction of the Hom-Yetter-Drinfeld category

Colloquium Mathematicae (2014)

- Volume: 137, Issue: 1, page 43-65
- ISSN: 0010-1354

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topHaiying Li, and Tianshui Ma. "A construction of the Hom-Yetter-Drinfeld category." Colloquium Mathematicae 137.1 (2014): 43-65. <http://eudml.org/doc/283988>.

@article{HaiyingLi2014,

abstract = {In continuation of our recent work about smash product Hom-Hopf algebras [Colloq. Math. 134 (2014)], we introduce the Hom-Yetter-Drinfeld category $_\{H\}^\{H\}$ via the Radford biproduct Hom-Hopf algebra, and prove that Hom-Yetter-Drinfeld modules can provide solutions of the Hom-Yang-Baxter equation and $_\{H\}^\{H\}$ is a pre-braided tensor category, where (H,β,S) is a Hom-Hopf algebra. Furthermore, we show that $(A♮_\{⋄\} H,α⊗ β)$ is a Radford biproduct Hom-Hopf algebra if and only if (A,α) is a Hom-Hopf algebra in the category $_\{H\}^\{H\}$. Finally, some examples and applications are given.},

author = {Haiying Li, Tianshui Ma},

journal = {Colloquium Mathematicae},

keywords = {Hom-Hopf algebras; Hom-smash products; Hom-smash coproducts; Hom-Yetter-Drinfeld categories; Radford biproducts; Hom-Yang-Baxter equation},

language = {eng},

number = {1},

pages = {43-65},

title = {A construction of the Hom-Yetter-Drinfeld category},

url = {http://eudml.org/doc/283988},

volume = {137},

year = {2014},

}

TY - JOUR

AU - Haiying Li

AU - Tianshui Ma

TI - A construction of the Hom-Yetter-Drinfeld category

JO - Colloquium Mathematicae

PY - 2014

VL - 137

IS - 1

SP - 43

EP - 65

AB - In continuation of our recent work about smash product Hom-Hopf algebras [Colloq. Math. 134 (2014)], we introduce the Hom-Yetter-Drinfeld category $_{H}^{H}$ via the Radford biproduct Hom-Hopf algebra, and prove that Hom-Yetter-Drinfeld modules can provide solutions of the Hom-Yang-Baxter equation and $_{H}^{H}$ is a pre-braided tensor category, where (H,β,S) is a Hom-Hopf algebra. Furthermore, we show that $(A♮_{⋄} H,α⊗ β)$ is a Radford biproduct Hom-Hopf algebra if and only if (A,α) is a Hom-Hopf algebra in the category $_{H}^{H}$. Finally, some examples and applications are given.

LA - eng

KW - Hom-Hopf algebras; Hom-smash products; Hom-smash coproducts; Hom-Yetter-Drinfeld categories; Radford biproducts; Hom-Yang-Baxter equation

UR - http://eudml.org/doc/283988

ER -

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