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

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

2007-09-20

arxiv.org/abs/0709.3170v2

Mathematics

Operator Algebras

Scientific paper

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 $n
\times n$ matrices of real polynomials is proved.

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