A construction of the Hom-Yetter-Drinfeld category

Haiying 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 -