The images of non-commutative polynomials evaluated on 2 × 2 matrices over an arbitrary field

DOI10.1142/S0219498814500042zbMath1300.16022arXiv1310.8563OpenAlexW2964121942MaRDI QIDQ5420672

Publication date: 13 June 2014

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.8563

zbMATH Keywords

matrix algebras Kaplansky-Lvov conjecture multilinear polynomials range of polynomials polynomial images non-commutative polynomials invariant cones of matrices

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Polynomials in general fields (irreducibility, etc.) (12E05) Trace rings and invariant theory (associative rings and algebras) (16R30) Special polynomials in general fields (12E10)

Related Items (23)

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 solutions of second-order matrix polynomial equation of high degree ⋮ Evaluations of multilinear polynomials on low rank Jordan algebras ⋮ On the Mesyan conjecture ⋮ Images of multilinear graded polynomials on upper triangular matrix algebras ⋮ Values of multilinear graded \(\ast\)-polynomials on upper triangular matrices of small dimension ⋮ A new approach to the Lvov-Kaplansky conjecture through gradings ⋮ The images of multilinear and semihomogeneous polynomials on the algebra of octonions ⋮ On the images of multilinear maps of matrices over finite-dimensional division algebras ⋮ Power-central polynomials on 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 ⋮ On the combinatorics of commutators of Lie algebras ⋮ The image of multilinear polynomials evaluated on \(3 \times 3\) upper triangular matrices ⋮ The images of noncommutative polynomials evaluated on the quaternion algebra ⋮ On the images of Jordan polynomials evaluated over symmetric matrices ⋮ Lvov-Kaplansky conjecture on UT_m^+ with the transpose involution ⋮ On Fagundes-Mello conjecture ⋮ Geometry of word equations in simple algebraic groups over special fields ⋮ Images of graded polynomials on matrix algebras

Cites Work

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