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

Shuangjian Guo; Shengxiang Wang

Colloquium Mathematicae, Tome 144 (2016), p. 169-185 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $B = A^{c o H}$ . Under the assumption that there exists a total quantum integral γ: H → Hom(H,A) and the canonical map $β : A \otimes_{B} A \to A \otimes H$ , $a \otimes_{B} b \mapsto S^{- 1} (b_{[1]}) α (b_{[0] [- 1]}) \otimes β^{- 1} (a) β (b_{[0] [0]})$ , is surjective, we prove that the induction functor $A \otimes_{B} - : ̃ {(_{k})}_{B} \to_{A}^{H}$ is an equivalence of categories.

Publié le : 2016-01-01

Zbl 06574980

EUDML-ID : urn:eudml:doc:284044

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     title = {The affineness criterion for quantum Hom-Yetter-Drinfel'd modules},
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     year = {2016},
     pages = {169-185},
     zbl = {06574980},
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Shuangjian Guo; Shengxiang Wang. The affineness criterion for quantum Hom-Yetter-Drinfel'd modules. Colloquium Mathematicae, Tome 144 (2016) pp. 169-185. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6609-12-2015/