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Galois Correspondences for Hopf Bigalois Extensions

✍ Scribed by Peter Schauenburg

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 228 KB
Volume: 201
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1997.7237

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✦ Synopsis

Let H be a Hopf algebra with bijective antipode over a commutative ring k. A right H-Galois extension of k is a right H-comodule algebra A such that k s A co H and a certain canonical map A m A ª A m H is a bijection. We investigate Galois connections for Hopf᎐Galois extensions that can be formulated with the help of an additional Hopf algebra L over which A is also a left L-Galois extension of k, and an L-H-bicomoduleᎏsuch an additional Hopf algebra always exists and is unique up to isomorphism. The Galois connection between quotient coalgebras and left modules of L and H-subcomodule algebras of A induces a bijection between those quotients over which L is faithfully coflat, and those subalgebras over which A is faithfully flat. As a consequence, the lattices of Hopf subalgebras of L and H over which these are faithfully flat are isomorphic.

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