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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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Hopf cohomology vanishing brought by approximating Hochschild cohomology
by
Akira Masuoka
Institute of Mathematics, University of Tsukuba

As a quantized (though weaker) result of the Levi decomposition for affine group schemes, we prove that if H is a (non-commutative) Hopf algebra whose coradical R is a Hopf subalgebra, the embedding of R into H splits as a left (or right) R-linear coalgebra map. This is based on the observation that the (non-abelian) Hopf cohomology can be approximated, in some sense, by the Hochschild cohomology. We prove also vanishing of such cohomologies in higher dimensions, that describe Hopf algebra extensions in dimension 2.

Date received: May 21, 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-23.