Primitive ideals in Hopf algebra extensions

Details Primitive ideals in Hopf algebra extensions Primitive ideals in Hopf algebra extensions

1998-08-28

arxiv.org/abs/math/9808122v1

Mathematics

Rings and Algebras

23 pages; written in LaTeX2e with pictures done by pb-diagran.sty

Scientific paper

Let $H$ be a finite-dimensional Hopf algebra. We study the behaviou r of primitive and maximal ideals in certain types of ring extensions determined by $H$. The main focus is on the class of faithfully flat Galois extensions, which includes includes smash and crossed products. It is shown how analogous results can be obtained for the larger class of extensions possessing a total integral, which includes extensions $A^H\subseteq A $ when $H$ is semisimple. We use Passman's "primitivity machine" to reduce the whole theory of Kr ull relations for prime ideals to the case of primitive ideals. The concept of strongly semiprimitive Hopf algebra is introduced and investigated. Several examples and open problems are discussed.

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