Non-commutative Real Algebraic Geometry - Some Basic Concepts and First Ideas

2007/09/20 by Konrad Schmuedgen, Schmuedgen, Konrad · 2 citations
Mathematics · #11E25 (Secondary) #13J30 #15A48 (Primary) #47L60 #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematics and Applications #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.0709.3170

openalex publication_date 2007/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose and discuss how basic notions (quadratic modules, positive elements, semialgebraic sets, Archimedean orderings) and results (Positivstellensaetze) from real algebraic geometry can be generalized to noncommutative *-algebras. A version of Stengle's Positivstellensatz for n × n matrices of real polynomials is proved.

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• Quantization of bounded symplectic domains associated with compact Lie groups
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