Zariski topologies on stratified spectra of quantum algebras

Brown, K. A. and Goodearl, K. R. (2015) Zariski topologies on stratified spectra of quantum algebras. In: Eisenbud, D. (ed.) Commutative Algebra and Noncommutative Algebraic Geometry. Series: Mathematical sciences research institute publications, 68 (68). Cambridge University Press, pp. 63-91. ISBN 9781107149724

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A framework is developed to describe the Zariski topologies on the prime and primitive spectra of a quantum algebra A in terms of the (known) topologies on strata of these spaces and maps between the collections of closed sets of different strata. A conjecture is formulated, under which the desired maps would arise from homomorphisms between certain central subalgebras of localized factor algebras of A. When the conjecture holds, spec A and prim A are then determined, as topological spaces, by a finite collection of (classical) affine algebraic varieties and morphisms between them. The conjecture is verified for Oq(GL2(k)), Oq(SL3(k)), and Oq(M2(k)) when q is a non-root of unity and the base field k is algebraically closed.

Item Type:Book Sections
Glasgow Author(s) Enlighten ID:Brown, Professor Ken
Authors: Brown, K. A., and Goodearl, K. R.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematical Sciences Research Institute Publications
Publisher:Cambridge University Press
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