Flatness and freeness properties of the generic Hopf Galois extensions

Abstract

In previous work, to each Hopf algebra H and each invertible right two-cocycle on H, Eli Aljadeff and the first-named author attached a subalgebra B of the free commutative Hopf algebra S generated by the coalgebra underlying H; the algebra B is the subalgebra of coinvariants of a generic Hopf Galois extension. In this paper we give conditions under which S is faithfully flat, or even free, as a B-module. We also show that B is generated as an algebra by certain elements arising from the theory of polynomial identities for comodule algebras developped jointly with Aljadeff.

15 pages. Corollary 3.7, Theorem 3.8, missing hypothesis in Theorem 3.13, and one reference added. Misprints corrected.

References in corpus (3)

• Polynomial identities and noncommutative versal torsors
• Construction of quantized enveloping algebras by cocycle deformation
• Cohomology of invariant Drinfeld twists on group algebras

Cited by in corpus (4)

• Hopf algebras and polynomial identities
• Generic base algebras and universal comodule algebras for some finite-dimensional Hopf algebras
• Principal fiber bundles in non-commutative geometry
• The Noether problem for Hopf algebras