Non-commutative varieties with curvature having bounded signature

zbMath1277.47026arXiv1202.0056MaRDI QIDQ351750

J. William Helton, Harry Dym, Scott A. McCullough

Publication date: 10 July 2013

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.0056

zbMATH Keywords

noncommutative polynomialsnoncommutative varieties

Mathematics Subject Classification ID

Linear operator inequalities (47A63) General theory of linear operators (47A99) Semialgebraic sets and related spaces (14P10) Convex sets and cones of operators (47L07)

Related Items (3)

Quasi-convex free polynomials ⋮ Noncommutative plurisubharmonic polynomials. I: Global assumptions ⋮ Noncommutative plurisubharmonic polynomials. II: Local assumptions

Uses Software

• NCAlgebra

Cites Work

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• Every convex free basic semi-algebraic set has an LMI representation
• Noncommutative convexity arises from linear matrix inequalities
• Classification of all noncommutative polynomials whose Hessian has negative signature one and a noncommutative second fundamental form
• Matrix inequalities: A symbolic procedure to determine convexity automatically
• The Hessian of a noncommutative polynomial has numerous negative eigenvalues
• Convex Noncommutative Polynomials Have Degree Two or Less
• Irreducible noncommutative defining polynomials for convex sets have degree 4 or less
• Operator theory on noncommutative varieties
• Non-commutative positive kernels and their matrix evaluations

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