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ISSN (electronic): 1464-8997
ISSN (print): 1464-8989

Hopf Galois theory: A survey

Susan Montgomery

Geometry & Topology Monographs 16 (2009) 367–400

DOI: 10.2140/gtm.2009.16.367

Abstract

We consider a Hopf Galois extension B A, for A a comodule algebra over the Hopf algebra H with coinvariant algebra B. After giving a number of examples, we discuss Galois extensions with additional properties, such as having a normal basis. We then consider when there is a category equivalence between the category of modules over B and the category of “relative Hopf modules” for A and H. Finally we discuss more recent work of van Oystaeyen and Zhang and of Schauenburg on obtaining correspondence theorems between suitable subalgebras of A and Hopf ideals of H.

Keywords

Hopf Galois extension, Galois correspondence

Mathematical Subject Classification

Primary: 16W30

Secondary: 16S34, 16S40

References
Publication

Received: 23 November 2009
Revised: 7 May 2009
Accepted: 8 June 2009
Published: 4 July 2009

Authors
Susan Montgomery
Mathematics Department
University of Southern California
Los Angeles, CA 90089-1113
USA