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||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 algebra; Involution; Quadratic form; Ordering; Trace; Noncommutative polynomial||Subject LCSH:||Forms, Quadratic
Rings with involution
|DOI:||10.1016/j.jalgebra.2010.03.022||Other versions:||http://dx.doi.org/10.1016/j.jalgebra.2010.03.022||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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