On the nonexistence of sum of squares certificates for the BMV conjecture

Kristijan Cafuta (kristijan.cafutafe.uni-lj.si)
Igor Klep (igor.klepfmf.uni-lj.si)
Janez Povh (janez.povhfis.unm.si)

Abstract: The algebraic reformulation of the BMV conjecture is equivalent to a family of dimensionfree tracial inequalities involving positive semidefinite matrices. Sufficient conditions for these to hold in the form of algebraic identities involving polynomials in noncommuting variables have been given by Markus Schweighofer and the second author. Later the existence of these certificates has been settled for all but one case, which is resolved in this short note.

Keywords: Bessis-Moussa-Villani (BMV) conjecture, noncommutative polynomial, sum of hermitian squares, commutator, cyclic equivalence, semidefinite programming

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Applications -- Science and Engineering (Basic Sciences Applications )

Citation: K. Cafuta, I. Klep, and J. Povh. A note on the nonexistence of sum of squares certicates for the Bessis-Moussa-Villani conjecture. J. math. phys., 51(8):083521, 10, 2010.

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Entry Submitted: 10/27/2009
Entry Accepted: 10/27/2009
Entry Last Modified: 03/21/2011

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