The affineness criterion for quantum Hom-Yetter-Drinfel'd modules

Shuangjian Guo, and Shengxiang Wang. "The affineness criterion for quantum Hom-Yetter-Drinfel'd modules." Colloquium Mathematicae 143.2 (2016): 169-185. <http://eudml.org/doc/284044>.

@article{ShuangjianGuo2016,
abstract = {Quantum integrals associated to quantum Hom-Yetter-Drinfel’d modules are defined, and the affineness criterion for quantum Hom-Yetter-Drinfel’d modules is proved in the following form. Let (H,α) be a monoidal Hom-Hopf algebra, (A,β) an (H,α)-Hom-bicomodule algebra and $B = A^\{coH\}$. Under the assumption that there exists a total quantum integral γ: H → Hom(H,A) and the canonical map $β: A ⊗_\{B\} A → A ⊗ H$, $a ⊗_\{B\} b↦ S^\{-1\}(b_\{[1]\})α(b_\{[0][-1]\}) ⊗ β^\{-1\}(a)β(b_\{[0][0]\})$, is surjective, we prove that the induction functor $A ⊗_\{B\}-: ̃ ( _\{k\})_\{B\} → ^\{H\} _\{A\}$ is an equivalence of categories.},
author = {Shuangjian Guo, Shengxiang Wang},
journal = {Colloquium Mathematicae},
keywords = {monoidal Hom-Hopf algebras; Hom-bicomodule algebras; total integrals; quantum Hom-Yetter-Drinfel'd modules},
language = {eng},
number = {2},
pages = {169-185},
title = {The affineness criterion for quantum Hom-Yetter-Drinfel'd modules},
url = {http://eudml.org/doc/284044},
volume = {143},
year = {2016},
}

TY - JOUR
AU - Shuangjian Guo
AU - Shengxiang Wang
TI - The affineness criterion for quantum Hom-Yetter-Drinfel'd modules
JO - Colloquium Mathematicae
PY - 2016
VL - 143
IS - 2
SP - 169
EP - 185
AB - Quantum integrals associated to quantum Hom-Yetter-Drinfel’d modules are defined, and the affineness criterion for quantum Hom-Yetter-Drinfel’d modules is proved in the following form. Let (H,α) be a monoidal Hom-Hopf algebra, (A,β) an (H,α)-Hom-bicomodule algebra and $B = A^{coH}$. Under the assumption that there exists a total quantum integral γ: H → Hom(H,A) and the canonical map $β: A ⊗_{B} A → A ⊗ H$, $a ⊗_{B} b↦ S^{-1}(b_{[1]})α(b_{[0][-1]}) ⊗ β^{-1}(a)β(b_{[0][0]})$, is surjective, we prove that the induction functor $A ⊗_{B}-: ̃ ( _{k})_{B} → ^{H} _{A}$ is an equivalence of categories.
LA - eng
KW - monoidal Hom-Hopf algebras; Hom-bicomodule algebras; total integrals; quantum Hom-Yetter-Drinfel'd modules
UR - http://eudml.org/doc/284044
ER -