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- W4298307918 abstract "Let A be a comodule algebra for a finite dimensional Hopf algebra K over an algebraically closed field k, and let A^K be the subalgebra of invariants. Let Z be a central subalgebra in A, which is a domain with quotient field Q. Assume that Qotimes_Z A is a central simple algebra over Q, and either A is a finitely generated torsion-free Z-module and Z is integrally closed in Q, or A is a finite projective Z-module. Then we show that A and Z are integral over the subring of central invariants Zcap A^K. More generally, we show that this statement is valid under the same assumptions if Z is a reduced algebra with quotient ring Q, and Qotimes_Z A is a semisimple algebra with center Q. In particular, the statement holds for a coaction of K on a prime PI algebra A whose center Z is an integrally closed finitely generated domain over k. This generalizes the results of S. Skryabin in the case when A is commutative. For the proof, we develop a theory of Galois bimodules over semisimple algebras finite over the center." @default.
- W4298307918 created "2022-10-02" @default.
- W4298307918 creator A5075556491 @default.
- W4298307918 date "2013-06-17" @default.
- W4298307918 modified "2023-10-17" @default.
- W4298307918 title "Galois bimodules and integrality of PI comodule algebras over invariants" @default.
- W4298307918 doi "https://doi.org/10.48550/arxiv.1306.3821" @default.
- W4298307918 hasPublicationYear "2013" @default.
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