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

Files in This Item:
File Description SizeFormat 
kups-04may09.pdf144.8 kBAdobe PDFDownload
Title: The Procesi-Schacher conjecture and Hilbert’s 17th problem for algebras with involution
Authors: Klep, Igor
Unger, Thomas
Permanent link: http://hdl.handle.net/10197/2432
Date: Jul-2010
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
Copyright (published version): 2010 Elsevier Inc
Keywords: Central simple algebra;Involution;Quadratic form;Ordering;Trace;Noncommutative polynomial
Subject LCSH: Forms, Quadratic
Rings with involution
Topological rings
Algebra
DOI: 10.1016/j.jalgebra.2010.03.022
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

Show full item record

SCOPUSTM   
Citations 50

3
Last Week
0
Last month
checked on Jun 22, 2018

Google ScholarTM

Check

Altmetric


This item is available under the Attribution-NonCommercial-NoDerivs 3.0 Ireland. No item may be reproduced for commercial purposes. For other possible restrictions on use please refer to the publisher's URL where this is made available, or to notes contained in the item itself. Other terms may apply.