# Non-commutative varieties with curvature having bounded signature

@article{Dym2011NoncommutativeVW, title={Non-commutative varieties with curvature having bounded signature}, author={Harry Dym and J. William Helton and Scott A. McCullough}, journal={arXiv: Functional Analysis}, year={2011} }

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.

## 4 Citations

Noncommutative Plurisubharmonic Polynomials Part I: Global Assumptions

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We consider symmetric polynomials, p, in the noncommutative free variables (x_1, x_2, ..., x_g). We define the noncommutative complex hessian of p and we call a noncommutative symmetric polynomial…

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This chapter is a tutorial on techniques and results in free convex algebraic geometry and free real algebraic geometry (RAG). The term free refers to the central role played by algebras of…

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Abstract We consider symmetric polynomials, p, in the noncommutative (nc) free variables { x 1 , x 2 , … , x g } . We define the nc complex hessian of p as the second directional derivative…

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Let $\Rx$ denote the ring of polynomials in $g$ freely non-commuting variables $x=(x_1,...,x_g)$. There is a natural involution * on $\Rx$ determined by $x_j^*=x_j$ and $(pq)^*=q^* p^*$ and a free…

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