Polarization algebras and their relations

DOI10.1216/JCA-2019-11-3-433zbMath1445.14084arXiv1412.2365OpenAlexW2992442701MaRDI QIDQ2011280

Ualbei Utmakhanbetovich Umirbaev

Publication date: 6 December 2019

Published in: Journal of Commutative Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.2365

zbMATH Keywords

Jacobian conjecturepolynomial mappingsEngel algebrashomogeneous dependencenilpotent and solvable algebras

Mathematics Subject Classification ID

Jacobian problem (14R15) Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) (14R10) Automorphisms, derivations, other operators (nonassociative rings and algebras) (17A36) Free nonassociative algebras (17A50) Ternary compositions (17A40)

Related Items (4)

The space of invariant bilinear forms of the polarization algebra of a polynomial endomorphism: an approach to the problem of Albert ⋮ On power-associative modules ⋮ About nilalgebras satisfying (xy)² = x²y² ⋮ Embedding of \(\mathfrak{sl}_2(\mathbb{C})\)-modules into four-dimensional power-associative zero-algebra modules

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An algorithm for associative bilinear forms
• Commutative finitely generated algebras satisfying \(((yx)x)x=0\) are solvable
• Keller's problem
• A Jacobian criterion for separability
• On the solvability of the commutative power-associative nilalgebras of dimension 6.
• Polynomial automorphisms and the Jacobian conjecture
• Schreier varieties of algebras
• On nilalgebras and linear varieties of nilpotent matrices. II
• On Commutative Power-Associative Nilalgebras
• The Jacobian conjecture: Reduction of degree and formal expansion of the inverse
• Commutative Finite-Dimensional Algebras Satisfyingx(x(xy)) = 0 are Nilpotent
• The formal inverse and the Jacobian Conjecture
• On Commutative Power-Associative Nilalgebras of Low Dimension
• Yagzhev polynomial mappings: on the structure of the Taylor expansion of their local inverse
• Classification of Quadratic Homogeneous Automorphisms in Dimension Five
• Quasi-translations and counterexamples to the Homogeneous Dependence Problem
• Power-associative rings

This page was built for publication: Polarization algebras and their relations