Nilpotent symmetric Jacobian matrices and the Jacobian conjecture

DOI10.1016/j.jpaa.2004.03.003zbMath1054.14083OpenAlexW2113637689MaRDI QIDQ1877754

Michiel de Bondt, A. R. P. van den Essen

Publication date: 19 August 2004

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2004.03.003

zbMATH Keywords

symmetric dependence problem

Mathematics Subject Classification ID

Jacobian problem (14R15) Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) (14R10)

Related Items (12)

Singular Hessians ⋮ The Jacobian conjecture, the \(d\)-inversion approximation and its natural boundary ⋮ Two results on homogeneous Hessian nilpotent polynomials ⋮ Legendre transform, Hessian conjecture and tree formula ⋮ Nilpotent symmetric Jacobian matrices and the Jacobian conjecture. II ⋮ Inversion problem, Legendre transform and inviscid Burgers equations ⋮ A reduction of the Jacobian Conjecture to the symmetric case ⋮ On the generalized vanishing conjecture ⋮ Hessian nilpotent polynomials and the Jacobian conjecture ⋮ Periodic multivariate formal power series ⋮ Polynomials with constant Hessian determinants in dimension three ⋮ Some results on the vanishing conjecture of differential operators with constant coefficients

Cites Work

• The Jacobian conjecture for symmetric Jacobian matrices.
• Polynomial automorphisms and the Jacobian conjecture
• The discrete Markus–Yamabe problem
• A reduction of the Jacobian Conjecture to the symmetric case
• Unnamed Item

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