The Generalized C.M.Z.-Theorem and a Drinfel'd Double Construction for WT-Coalgebras and Graded Quantum Groupoids

摘要

Let π be a group. In this article, we introduce the notions of a weak Doi-Hopf π-module and a weak π-twisted smash product. We show that the Yetter-Drinfel'd π-modules over a weak crossed Hopf π-coalgebra (WT-coalgebra) are special cases as these new weak Doi-Hopf π-modules, generalizing the main result by Caenepeel et al. (19972. Caenepeel , S. , Militaru , G. , Zhu , S. ( 1997 ). Crossed modules and Doi-Hopf modules . Israel J. Math. 100 : 221 - 248 .[CrossRef], [Web of Science ®]View all references) and that the Drinfel'd double for WT-coalgebras (Van Daele and Wang, 200812. Van Daele , A. , Wang , S. H. ( 2008 ). New braided crossed categories and Drinfel'd quantum double for weak Hopf group-coalgebras . Comm. Algebra 36 : 2341 - 2386 .[Taylor & Francis Online], [Web of Science ®]View all references) appears as, a type of such a weak π -twisted smash product, respectively. Finally, starting from a weak Hopf algebra endowed with an action of a group π by weak Hopf automorphisms, we construct a quasitriangular weak Hopf π -coalgebra by a twisted double method, generalizing the main result in Virelizier (200514. Virelizier , A. ( 2005 ). Graded quantum groups and quasitriangular Hopf group-coalgebras . Comm. Algebra 33 ( 9 ): 3029 - 3050 .[Taylor & Francis Online], [Web of Science ®]View all references). This method allows us to obtain nontrivial examples of quasitriangular weak Hopf π-coalgebras.View full textDownload full textKey WordsDrinfel'd double, Graded quantum groupoids, Weak Doi-Hopf π-module, Weak Hopf π -coalgebra, Weak π -twisted smash product2000 Mathematics Subject Classification16W30Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927870802107611