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Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories
September 23-28, 2002
Fields Institute
Toronto, ON, Canada

Organizers
George Janelidze, Georgian Academy of Sciences, Bodo Pareigis, University of Munich, Walter Tholen, York University

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On cohomology of Hopf algebroids
by
Masoud Khalkhali
Department of Mathematics, University of Western Ontario, London ON Canada
Coauthors: B. Rangipour (Western Ontario)

Inspired by the work of Connes and Moscovici, we introduce the concept of extended Hopf algebra and consider their cyclic cohomology in the spirit of Connes-Moscovici's cyclic cohomology for Hopf algebras. Extended Hopf algebras are closely related, but different from, Hopf algebroids. Their definition is motivated by attempting to define cyclic cohomology of Hopf algebroids in general. Many of Hopf algebra like structures, including the Connes-Moscovici algebra HFM are extended Hopf algebras. We show that the cyclic cohomology of the extended Hopf algebra U(L, R) naturally associated to a Lie-Rinehart algebra (L, R) coincides with the homology of (L, R). We also give some other examples of extended Hopf algebras and their cyclic cohomology.

Paper reference: arXiv:math.KT/0105105

Date received: May 27, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajf-26.