On generalized Hopf galois extensions

By Peter Schauenburg, Hans-Jürgen Schneider. 2004

58 citations recorded by the source corpus.

Abstract The key part of the definition of a Hopf-Galois extension B ⊂ A over the Hopf algebra H is bijectivity of a canonical map β : A ⊗ B A → A ⊗ H . We develop criteria under which surjectivity of β (which is usually much easier to verify) is sufficient, and we investigate the consequences for the structure of A as a B -module and H -comodule. In particular, we prove equivariant projectivity of extensions in several important cases. We study these questions for generalizations of H -Galois extensions like Q -Galois extensions for a quotient coalgebra and one-sided module of a Hopf algebra H , and coalgebra Galois extensions.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ae680f7806b64b4b22bf7438a31989fefffdbfb2

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In Algebra and Number Theory

1. P. M. Hajac
2. Bartosz Zielinski
3. R. Matthes
4. U. Kraehmer

In Geometry and Topology

1. P. M. Hajac
2. Bartosz Zielinski
3. R. Matthes
4. U. Kraehmer

In Statistical and Nonlinear Physics

1. P. M. Hajac
2. Bartosz Zielinski
3. R. Matthes
4. U. Kraehmer

Citations in the corpus

• Piecewise principal comodule algebras (2007, methodology): “The notion of locality we use herein results from decomposing algebras into “pieces”, meaning expressing them as multiple fibre products (called multirestricted direct sums in [26, p. 264]).”