Noetherian Centralizing Hopf Algebra Extensions and Finite Morphisms of Quantum Groups
Abstract
Description
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.
To appear in Bulletin of the London Mathematical Society
To appear in Bulletin of the London Mathematical Society