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

• Autorzy: Shuangjian Guo , Shengxiang Wang
• Języki publikacji: EN

Abstrakty

EN

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 $A ⊗_{B}-: 𝓗̃ (𝓜 _{k})_{B} → ^{H}𝓗 𝓨 𝓓_{A}$ is an equivalence of categories.

Kategorie tematyczne

• 16T05: Hopf algebras and their applications

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 143
• Numer: 2
• Strony: 169-185

Daty

wydano

2016

Twórcy

autor

Shuangjian Guo

• School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, 550025, P.R. China

autor

Shengxiang Wang

• School of Mathematics and Finance, Chuzhou University, Chuzhou 239000, P.R. China

Identyfikatory

DOI

10.4064/cm6609-12-2015