Non-commutative varieties with curvature having bounded signature

2012/02/01 by Harry Dym, J. William Helton, Dym, Harry +3
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1202.0056

arxiv created 2012/02/01 · arxiv updated 2012/02/02

Abstract

The signature(s) of the curvature of the zero set V of a free (non-commutative) polynomial is defined as the number of positive and negative eigenvalues of the non-commutative second fundamental form on V determined by p. With some natural hypotheses, the degree of p is bounded in terms of the signature. In particular, if one of the signatures is zero, then the degree of p is at most two.

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