Quantum n-space as a quotient of classical n-space

1999/05/10 by K. R. Goodearl, Goodearl, K. R., Edward S. Letzter +2
Mathematics · #16D30 #16D60 #16P40 #16S36 #17B37 #81R50 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:16D30 #msc:16D60 #msc:16P40 #msc:16S36 #msc:17B37 #msc:81R50

paper · pdf · doi:10.48550/arxiv.math/9905055

24 pages

arxiv created 1999/05/10 · openalex publication_date 1999/05/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A denote the commutative polynomial ring in n variables, over an algebraically closed field k, and let R denote the standard multiparameter quantization of A determined by a multiplicatively antisymmetric n× n matrix (q_ij). In this paper we prove, when -1 cannot be multiplicatively generated by the q_ij, that the primitive spectrum of R is a topological quotient of kⁿ. Under the same hypothesis, we further prove that the prime spectrum of R is a topological quotient of the prime spectrum of A.

Citations

• Algebraic structure of multi-parameter quantum groups

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