Quantized primitive ideal spaces as quotients of affine algebraic varieties

1999/12/14 by K. R. Goodearl, Goodearl, K. R.
Mathematics · Physics and Astronomy · #16D30 #16D60 #16P40 #16S36 #17B37 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:16D30 #msc:16D60 #msc:16P40 #msc:16S36 #msc:17B37

paper · pdf · doi:10.48550/arxiv.math/9912110

17 pages

arxiv created 1999/12/14 · openalex publication_date 1999/12/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given an affine algebraic variety V and a quantization A of its coordinate ring, it is conjectured that the primitive ideal space of A can be expressed as a topological quotient of V. Evidence in favor of this conjecture is discussed, and positive solutions for several types of varieties (obtained in joint work with E. S. Letzter) are described. In particular, explicit topological quotient maps are given in the case of quantum toric varieties.

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