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Projectivity of Hopf algebras over subalgebras with semilocal central localizations

Published online by Cambridge University Press:  11 January 2008

Serge Skryabin
Serge Skryabin
Affiliation:
Serge.Skryabin@ksu.ruChebotarev Research Institute, Universitetskaya St. 17, 420008 Kazan, Russia
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Abstract

The purpose of this paper is to extend the class of pairs A, H where H is a Hopf algebra over a field and A a right coideal subalgebra for which H is proved to be either projective or flat as an A-module. The projectivity is obtained under the assumption that H is residually finite dimensional, A has semilocal localizations with respect to a central subring, and there exists a Hopf subalgebra B of H such that the antipode of B is bijective and B is a finitely generated A-module. The flatness of H over A is shown to hold when H is a directed union of residually finite dimensional Hopf subalgebras, and there exists a Hopf subalgebra of H whose center contains A. More general projectivity and flatness results are established for (co)equivariant modules over an H-(co)module algebra under similar assumptions.

Keywords

Hopf algebrasModule algebrasComodule algebrasCoideal subalgebrasProjective modulesFlat modules
Type
Research Article
Information
Journal of K-Theory , Volume 2 , Issue 1 , August 2008 , pp. 1 - 40
Copyright
Copyright © ISOPP 2008

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