Non-commutative varieties with curvature having bounded signature. (English) Zbl 1277.47026

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

Ill. J. Math. 55, No. 2, 427-464 (2011).

One of the aims of this paper is to introduce a notion of signature of the curvature of the zero set \(V(p)\) of a non-commutative polynomial \(p\) and to prove a lower bound in terms of the degree of the polynomial. It follows that, if the non-commutative variety \(V(p)\) has positive curvature, then the degree of \(p\) is at most two. A new version of a non-commutative analogue of the Hessian of \(p\) is also discussed.

Reviewer: Cătălin Badea (Villeneuve d’Ascq)

MSC:

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

Keywords:

noncommutative varieties; noncommutative polynomials

Citations:

Zbl 1128.47020; Zbl 1206.47007

Software:

NCAlgebra

References:

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