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2019 Polarization algebras and their relations
Ualbai Umirbaev
J. Commut. Algebra 11(3): 433-451 (2019). DOI: 10.1216/JCA-2019-11-3-433

Abstract

Using an approach to the Jacobian conjecture by L.M. Druzkowski and K. Rusek, G. Gorni and G. Zampieri, and A.V. Yagzhev, we describe a correspondence between finite dimensional symmetric algebras and homogeneous tuples of elements of polynomial algebras. We show that this correspondence closely relates Albert's problem in classical ring theory and the homogeneous dependence problem in affine algebraic geometry related to the Jacobian conjecture. We demonstrate these relations in concrete examples and formulate some open questions.

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Ualbai Umirbaev. "Polarization algebras and their relations." J. Commut. Algebra 11 (3) 433 - 451, 2019. https://doi.org/10.1216/JCA-2019-11-3-433

Information

Published: 2019
First available in Project Euclid: 3 December 2019

zbMATH: 07140755
MathSciNet: MR4038058
Digital Object Identifier: 10.1216/JCA-2019-11-3-433

Subjects:
Primary: 14R15 , 17A40 , 17A50
Secondary: 14R10 , 17A36

Keywords: Engel algebras , homogeneous dependence , Jacobian conjecture , nilpotent and solvable algebras , polynomial mappings

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.11 • No. 3 • 2019
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