Dingguo Wang

Publications (2)0 Total impact

• Source

  Available from: arxiv.org

  Article: Yetter-Drinfeld modules over weak bialgebras

  S. Caenepeel, Dingguo Wang, Yanmin Yin
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  ABSTRACT: We discuss properties of Yetter-Drinfeld modules over weak bialgebras over commutative rings. The categories of left-left, left-right, right-left and right-right Yetter-Drinfeld modules over a weak Hopf algebra are isomorphic as braided monoidal categories. Yetter-Drinfeld modules can be viewed as weak Doi-Hopf modules, and, a fortiori, as weak entwined modules. IfH is finitely generated and projective, then we introduce the Drinfeld double using duality results between entwining structures and smash product structures, and show that the category of Yetter-Drinfeld modules is isomorphic to the category of modules over the Drinfeld double. The category of finitely generated projective Yetter-Drinfeld modules over a weak Hopf algebra has duality. Si esaminano le proprietà dei moduli Yetter-Drinfeld su weak bialgebre su anelli commutativi. Le categorie dei moduli Yetter-Drinfield sinistri-sinistri, sinistri-destri, destri-sinistri e destri-destri su di una weak Hopf algebra sono isomorfe come categorie monoidali braided. I moduli Yetter-Dinfeld possono essere riguardanti come weak Doi-Hopf moduli e, a fortiori, come moduli weak entwined. Nel caso in cuiH è finitamente generata e proiettiva, utilizzando risultati di dualità tra le strutture entwining e le strutture di prodotto smash, viene introdotto il Drinfeld double e si dimostra che la categoria dei moduli Yetter-Drinfeld è isomorfa alla categoria dei moduli sul Drinfeld double. Nel caso di una weak Hopf algebra, la categoria dei moduli Yetter-Drinfeld finitamente generati e proiettivi ha dualità.
  Annali dell'Università di Ferrara. Sezione 7: Scienze matematiche 04/2012; 51(1):69-98.
• Source

  Available from: ArXiv

  Article: Yetter-Drinfeld modules over weak Hopf algebras and the center construction

  S. Caenepeel, Dingguo Wang, Yanmin Yin
  [show abstract] [hide abstract]
  ABSTRACT: We introduce Yetter-Drinfeld modules over a weak Hopf algebra $H$, and show that the category of Yetter-Drinfeld modules is isomorphic to the center of the category of $H$-modules. The categories of left-left, left-right, right-left and right-right Yetter-Drinfeld modules are isomorphic as braided monoidal categories. Yetter-Drinfeld modules can be viewed as weak Doi-Hopf modules, and, a fortiori, as weak entwined modules. If $H$ is finitely generated and projective, then we introduce the Drinfeld double using duality results between entwining structures and smash product structures, and show that the category of Yetter-Drinfeld modules is isomorphic to the category of modules over the Drinfeld double.
  10/2004;