Projectivity and freeness over comodule algebras

By S. Skryabin. 2006

101 citations recorded by the source corpus.

Let H be a Hopf algebra and A an H-simple right H-comodule algebra. It is shown that under certain hypotheses every (H, A)-Hopf module is either projective or free as an A-module and A is either a quasi-Frobenius or a semisimple ring. As an application it is proved that every weakly finite (in particular, every finite dimensional) Hopf algebra is free both as a left and a right module over its finite dimensional right coideal subalgebras, and the latter are Frobenius algebras. Similar results are obtained for H-simple H-module algebras.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/face09535b96ead52f5c7bbf653448d73d221641

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Citations in the corpus

On module categories over finite-dimensional Hopf algebras (2006, result): “LE CATEGORIES OVER HOPF ALGEBRAS 5 1.2. Freeness over comodule algebras. Let Hbe a ﬁnite dimensional Hopf algebra. In this subsection we recall some important results obtained recently by S. Skryabin [S]. Theorem 1.4. Let Abe a ﬁnite dimensional right H-comodule algebra. Assume that Ais H-simple. Th”
On the Hochschild (co)homology of quantum homogeneous spaces (2008, result): “It is always satisfied in the commutative case [31], note also the recent results of Skryabin [38].”