Noncommutative Real Algebraic Geometry Some Basic Concepts and First Ideas

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


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.

Key words

Noncommutative real algebraic geometry quadratic module, sum of squares *-representation positivity positive semidefinite matrices 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Konrad Schmüdgen
    • 1
  1. 1.Fakultät für Mathematik und InformatikUniversität LeipzigLeipzigGermany

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