Noetherian Centralizing Hopf Algebra Extensions and Finite Morphisms of Quantum Groups

Details Noetherian Centralizing Hopf Algebra Extensions and Finite Morphisms of Quantum Groups Noetherian Centralizing Hopf Algebra Extensions and Finite Morphisms of Quantum Groups

1999-05-10

arxiv.org/abs/math/9905056v1

Mathematics

Rings and Algebras

To appear in Bulletin of the London Mathematical Society

Scientific paper

Let $A \subset H$ be a finite centralizing extension of noetherian Hopf algebras, and let $X$ denote the group of characters of $H$ that restrict to the augmentation map on $A$. Our main results provide necessary and sufficient conditions for the fibers of the canonical surjection from $spec H$ onto $spec A$ to coincide with the $X$-orbits in $spec H$. In particular, all of the fibers are $X$-orbits if and only if the fiber over the augmentation ideal of $A$ is an $X$-orbit. An application to the representation theory of quantum function algebras, at roots of unity, is presented.

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