Geodesic
The image of multilinear polynomials evaluated on $3\times 3$ upper triangular matrices
Communications in Mathematics, Tome 29 (2021) no. 2, pp. 183-186 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We describe the images of multilinear polynomials of arbitrary degree evaluated on the $3\times 3$ upper triangular matrix algebra over an infinite field.
We describe the images of multilinear polynomials of arbitrary degree evaluated on the $3\times 3$ upper triangular matrix algebra over an infinite field.
Classification : 16R10, 16S50
Keywords: multilinear polynomials; upper triangular matrices; Lvov-Kaplansky's conjecture 
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Mello, Thiago Castilho de. The image of multilinear polynomials evaluated on $3\times 3$ upper triangular matrices. Communications in Mathematics, Tome 29 (2021) no. 2, pp. 183-186. http://geodesic.mathdoc.fr/item/COMIM_2021_29_2_a2/

[1] Drensky, V.: Free Algebras and PI-Algebras. Graduate course in algebra. 2000, Springer-Verlag,

[2] Fagundes, P. S.: Imagens De Polinômios Multilineares Sobre Algumas Subálgebras de Matrizes. 2019, Dissertação de Mestrado em Matemática Aplicada, Universidade Federal de São Paulo.

[3] Fagundes, P. S.: The images of multilinear polynomials on strictly upper triangular matrices. Linear Algebra Appl., 563, 2019, 287-301, | DOI

[4] Fagundes, P.S., Mello, T.C. de: Images of multilinear polynomials of degree up to four on upper triangular matrices. Oper. Matrices, 13, 1, 2019, 283-292, | DOI

[5] Filippov, V.T., Kharchenko, V.K., Shestakov, I.P.: Dniester notebook: unsolved problems in the theory of rings and modules. Non-associative algebra and its applications, Lect. Notes Pure Appl. Math. 246, 2006, 461-516, Chapman & Hall/CRC, Translated from the 1993 Russian edition by Murray R. Bremner and Mikhail V. Kochetov. | DOI

[6] Kanel-Belov, A., Malev, S., Rowen, L.: The images of non-commutative polynomials evaluated on $2\times 2$ matrices. Proc. Amer. Math. Soc., 140, 2012, 465-478, | DOI

[7] Kanel-Belov, A., Malev, S., Rowen, L.: The images of non-commutative polynomials evaluated on $3\times 3$ matrices. Proc. Amer. Math. Soc., 144, 2016, 7-19, | DOI

[8] Kanel-Belov, A., Malev, S., Rowen, L.: Evaluations of Noncommutative Polynomials on Finite Dimensional Algebras. L\IL2\textquoteright vov-Kaplansky Conjecture. SIGMA, 16, 2020, 61 pp,

[9] Malev, A.: The image of non-commutative polynomials evaluated on $2\times 2$ matrices over an arbitrary field. J. Algebra Appl., 13, 6, 2014, 12 pp,

[10] Wang, Y.: The images of multilinear polynomials on $2 \times 2$ upper triangular matrix algebras. Linear and Multilinear Algebra, 67, 11, 2019, 2366-2372, | DOI

[11] Wang, Y., Liu, P., Bai, J.: The images of multilinear polynomials on $2 \times 2$ upper triangular matrix algebras (Correction). Linear and Multilinear Algebra, 67, 11, 2019, i-vi,