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Prime ideals in Hopf galois extensions

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Abstract

For a finite-dimensional Hopf algebraH, we study the prime ideals in a faithfully flatH-Hopf-Galois extensionR ⊂A. One application is to quotients of Hopf algebras which arise in the theory of quantum groups at a root of 1. For the Krull relations betweenR andA, we obtain our best results whenH is semisolvable; these results generalize earlier known results for crossed products for a group action and for algebras graded by a finite group. We also show that ifH is semisimple and semisolvable, thenA is semiprime providedR isH-semiprime.

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Authors and Affiliations

  1. Department of Mathematics, University of Southern California, 90089-1113, Los Angeles, CA, USA

    S. Montgomery

  2. Mathematisches Institut, Universität München, Theresienstraße 39, D-80333, Munich, Germany

    H. -J. Schneider

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  1. S. Montgomery
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  2. H. -J. Schneider
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Correspondence to S. Montgomery.

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Montgomery, S., Schneider, H.J. Prime ideals in Hopf galois extensions. Isr. J. Math. 112, 187–235 (1999). https://doi.org/10.1007/BF02773482

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  • DOI: https://doi.org/10.1007/BF02773482

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