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Emerging Applications of Algebraic Geometry pp 325–350Cite as

Noncommutative Real Algebraic Geometry Some Basic Concepts and First Ideas

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Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 149))

Abstract

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

AMS(MOS) subject classifications. Primary: 13J30, 47L60, 15A48; Secondary: l1E25.

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik und Informatik, Universität Leipzig, Leipzig, Germany

    Konrad Schmüdgen

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  1. Konrad Schmüdgen
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Editors and Affiliations

  1. College of Letters & Science, Dept. Mathematics, University of California, Santa Barbara, Santa Barbara, 93106, California, USA

    Mihai Putinar

  2. Department of Mathematics Harvard University, Cambridge, 02138, U.S.A.

    Seth Sullivant

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Schmüdgen, K. (2009). Noncommutative Real Algebraic Geometry Some Basic Concepts and First Ideas. In: Putinar, M., Sullivant, S. (eds) Emerging Applications of Algebraic Geometry. The IMA Volumes in Mathematics and its Applications, vol 149. Springer, New York, NY. https://doi.org/10.1007/978-0-387-09686-5_9

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