The Procesi-Schacher conjecture and Hilbert’s 17th problem for algebras with involution

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Title: The Procesi-Schacher conjecture and Hilbert’s 17th problem for algebras with involution
Authors: Klep, Igor
Unger, Thomas
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Date: Jul-2010
Online since: 2010-08-24T15:42:24Z
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.
Funding Details: Science Foundation Ireland
Type of material: Journal Article
Publisher: Elsevier
Journal: Journal of Algebra
Volume: 324
Issue: 2
Start page: 256
End page: 268
Copyright (published version): 2010 Elsevier Inc
Keywords: Central simple algebraInvolutionQuadratic formOrderingTraceNoncommutative polynomial
Subject LCSH: Forms, Quadratic
Rings with involution
Topological rings
DOI: 10.1016/j.jalgebra.2010.03.022
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Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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