On the images of Lie polynomials evaluated on Lie algebras

DOI10.1016/j.laa.2014.11.015zbMath1366.17004OpenAlexW2061163386WikidataQ115344521 ScholiaQ115344521MaRDI QIDQ486201

Zachary M. Emrich, Kaavya G. Valiveti, Benjamin E. Anzis

Publication date: 14 January 2015

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2014.11.015

zbMATH Keywords

Lie algebramultilinear Lie polynomial

Mathematics Subject Classification ID

Identities, free Lie (super)algebras (17B01) Simple, semisimple, reductive (super)algebras (17B20)

Related Items (15)

Instances of the Kaplansky-Lvov multilinear conjecture for polynomials of degree three ⋮ The images of polynomials on \(3 \times 3\) upper triangular matrix algebras ⋮ On the Mesyan conjecture ⋮ Polynomial identities and images of polynomials on null-filiform Leibniz algebras ⋮ On the images of multilinear maps of matrices over finite-dimensional division algebras ⋮ The images of multilinear polynomials on strictly upper triangular matrices ⋮ Evaluations of noncommutative polynomials on algebras: methods and problems, and the L'vov-Kaplansky conjecture ⋮ The image of polynomials on \(2\times 2\) upper triangular matrix algebras ⋮ The images of completely homogeneous polynomials on \(2\times 2\) upper triangular matrix algebras ⋮ Unnamed Item ⋮ On the images of Jordan polynomials evaluated over symmetric matrices ⋮ On Fagundes-Mello conjecture ⋮ Geometry of word equations in simple algebraic groups over special fields ⋮ The images of multilinear polynomials on 2 × 2 upper triangular matrix algebras ⋮ Image of Lie polynomial of degree 2 evaluated on nilpotent Lie algebra

Cites Work

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• Unnamed Item
• On the image of a noncommutative polynomial.
• On matrices of trace zero
• Normal forms for orthogonal similarity classes of skew-symmetric matrices
• Elements of reduced trace \(0\)
• On multilinear polynomials in four variables evaluated on matrices
• Polynomials of small degree evaluated on matrices
• The images of non-commutative polynomials evaluated on 2×2 matrices
• Commutators of nilpotent matrices
• On Commutators in a Simple Lie Algebra

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