Spectra of quantized hyperalgebras

Abstract

We describe the prime and primitive spectra for quantized enveloping algebras at roots of 1 in characteristic zero in terms of the prime spectrum of the underlying enveloping algebra. Our methods come from the theory of Hopf algebra crossed products. For primitive ideals we obtain an analogue of Duflo’s Theorem, which says that every primitive ideal is the annihilator of a simple highest weight module. This depends on an extension of Lusztig’s tensor product theorem.