Homological dimensions of smooth and complex analytic quantum tori

2009/07/04 by A. Yu. Pirkovskii, Pirkovskii, A. Yu. · 1 citation
Mathematics · #16E10 (Primary) #18G25 #46H25 (Secondary) #46M18 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.FA #math.QA #math.RA #msc:16E10 #msc:18G25 #msc:46H25 #msc:46M18

paper · pdf · doi:10.48550/arxiv.0907.0747

14 pages

arxiv created 2009/07/04 · openalex publication_date 2009/07/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We survey some results on homological dimensions of the algebraic, complex analytic, and smooth quantum tori. Our main theorem states, in particular, that the smooth and the complex analytic quantum n-tori have global dimension n. This contrasts with the result of McConnell and Pettit (1988) who proved that, in the generic case, the algebraic quantum n-torus has global dimension 1. In this connection we also formulate some general theorems on homological dimensions of nuclear Fréchet algebras.

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• Homological dimensions of algebras of analytic functionals and their completions

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