Abstract
The main goal of this chapter is to establish sufficient conditions for the DixmierMoeglin equivalence in a context that can be applied to quantized coordinate rings. By Lemma II.7.15, we have the implications
locally closed ⇉ primitive ⇉ rational
for prime ideals of a noetherian k-algebra satisfying the Nullstellensatz. In the original context of enveloping algebras, closing the loop - i.e., proving that rational primes are locally closed - was the most difficult of the three implications. In the context of quantized coordinate rings, we proceed by taking advantage of the stratifications which we have not yet exploited relative to primitive ideals. This adds another link to the chain above, and provides a third criterion for primitivity.
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© 2002 Springer Basel AG
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Brown, K.A., Goodearl, K.R. (2002). The Dixmier-Moeglin Equivalence. In: Lectures on Algebraic Quantum Groups. Advanced Courses in Mathematics CRM Barcelona. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8205-7_24
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DOI: https://doi.org/10.1007/978-3-0348-8205-7_24
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-6714-5
Online ISBN: 978-3-0348-8205-7
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