The Procesi-Schacher conjecture and Hilbert’s 17th problem for algebras with involution
|Title:||The Procesi-Schacher conjecture and Hilbert’s 17th problem for algebras with involution||Authors:||Klep, Igor
|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
|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
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.