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 matrices of real polynomials is proved.
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}
}