Images of multilinear polynomials of degree up to four on upper triangular matrices

DOI10.7153/oam-2019-13-18zbMath1432.16023arXiv1807.09421OpenAlexW2884432348WikidataQ128198444 ScholiaQ128198444MaRDI QIDQ5229264

Pedro S. Fagundes, Thiago Castilho de Mello

Publication date: 14 August 2019

Published in: Operators and Matrices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.09421

zbMATH Keywords

upper triangular matricesLvov-Kaplansky conjectureimages of polynomials

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Matrices over function rings in one or more variables (15A54)

Related Items (16)

Lie identities and images of Lie polynomials for the skew-symmetric elements of UT_m ⋮ The images of polynomials on \(3 \times 3\) upper triangular matrix algebras ⋮ On the Mesyan conjecture ⋮ Images of multilinear graded polynomials on upper triangular matrix algebras ⋮ The image of polynomials and Waring type problems on upper triangular matrix algebras ⋮ The image of polynomials in one variable on the algebra of \(3 \times 3\) upper triangular matrices ⋮ Images of multilinear polynomials on \(n \times n\) upper triangular matrices over infinite fields ⋮ 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 ⋮ The image of multilinear polynomials evaluated on \(3 \times 3\) upper triangular matrices ⋮ Lvov-Kaplansky conjecture on UT_m^+ with the transpose involution ⋮ On Fagundes-Mello conjecture ⋮ The images of multilinear polynomials on 2 × 2 upper triangular matrix algebras ⋮ The images of multilinear polynomials on 2 × 2 upper triangular matrix algebras

Cites Work

• On the image of a noncommutative polynomial.
• On matrices of trace zero
• Elements of reduced trace \(0\)
• On multilinear polynomials in four variables evaluated on matrices
• Konstanzelemente in Ringen mit Differentiation
• Polynomials of small degree evaluated on matrices
• The images of non-commutative polynomials evaluated on 2×2 matrices
• A Basis for Free Lie Rings and Higher Commutators in Free Groups
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