The Procesi-Schacher conjecture and Hilbert's 17th problem for algebras with involution
Rings and Algebras
2012-02-07 v2
Abstract
In 1976 Procesi and Schacher developed an Artin-Schreier type theory for central simple algebras with involution and conjectured that in such an algebra a totally positive element is always a sum of hermitian squares. In this paper elementary counterexamples to this conjecture are constructed and cases are studied where the conjecture does hold. Also, a Positivstellensatz is established for noncommutative polynomials, positive semidefinite on all tuples of matrices of a fixed size.
Cite
@article{arxiv.0810.5254,
title = {The Procesi-Schacher conjecture and Hilbert's 17th problem for algebras with involution},
author = {Igor Klep and Thomas Unger},
journal= {arXiv preprint arXiv:0810.5254},
year = {2012}
}
Comments
Final pre-publication version