The space of invariant bilinear forms of the polarization algebra of a polynomial endomorphism: an approach to the problem of Albert

DOI10.1016/j.jalgebra.2020.12.018zbMath1483.17002OpenAlexW3117528742MaRDI QIDQ2659107

Manuel J. Arenas

Publication date: 25 March 2021

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2020.12.018

zbMATH Keywords

Jacobian conjectureinvariant bilinear formsnon-associative algebrasnil-algebraspolynomial endomorphismssolvable algebrasproblem of Albert

Mathematics Subject Classification ID

Structure theory for nonassociative algebras (17A60) Jacobian problem (14R15) Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) (14R10) Power-associative rings (17A05) Automorphisms, derivations, other operators (nonassociative rings and algebras) (17A36)

Cites Work

• An algorithm for associative bilinear forms
• Commutative finitely generated algebras satisfying \(((yx)x)x=0\) are solvable
• Power-associative algebras with a nil basis
• Keller's problem
• On the solvability of the commutative power-associative nilalgebras of dimension 6.
• Polarization algebras and their relations
• On nilalgebras and linear varieties of nilpotent matrices. II
• On Commutative Power-Associative Nilalgebras
• Commutative Finite-Dimensional Algebras Satisfyingx(x(xy)) = 0 are Nilpotent
• Yagzhev polynomial mappings: on the structure of the Taylor expansion of their local inverse
• Quasi-translations and counterexamples to the Homogeneous Dependence Problem
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