English

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

Operator Algebras 2007-09-25 v2

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×nn \times n matrices of real polynomials is proved.

Keywords

Cite

@article{arxiv.0709.3170,
  title  = {Non-commutative Real Algebraic Geometry - Some Basic Concepts and First Ideas},
  author = {Konrad Schmuedgen},
  journal= {arXiv preprint arXiv:0709.3170},
  year   = {2007}
}
R2 v1 2026-06-21T09:19:24.080Z