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

Klep, Igor; Unger, T

dc.contributor.author	Klep, Igor	en
dc.contributor.author	Unger, T	en
dc.date.accessioned	2012-05-22T23:06:40Z	en
dc.date.issued	2010	en
dc.identifier.citation	Journal of Algebra 324(2):256-268 2010	en
dc.identifier.issn	0021-8693	en
dc.identifier.uri	http://hdl.handle.net/2292/18132	en
dc.description.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.	en
dc.publisher	Elsevier; Academic Press	en
dc.relation.ispartofseries	Journal of Algebra	en
dc.rights	Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from http://www.sherpa.ac.uk/romeo/issn/0021-8693/	en
dc.rights.uri	https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm	en
dc.title	The Procesi-Schacher conjecture and Hilbert's 17th problem for algebras with involution	en
dc.type	Journal Article	en
dc.identifier.doi	10.1016/j.jalgebra.2010.03.022	en
pubs.issue	2	en
pubs.begin-page	256	en
pubs.volume	324	en
dc.rights.holder	Copyright: Elsevier; Academic Press	en
pubs.end-page	268	en
dc.rights.accessrights	http://purl.org/eprint/accessRights/RestrictedAccess	en
pubs.subtype	Article	en
pubs.elements-id	243198	en
pubs.arxiv-id	0810.5254	en
dc.identifier.eissn	1090-266X	en
pubs.record-created-at-source-date	2012-05-23	en