The image of multilinear polynomials evaluated on 3 × 3 upper triangular matrices

Thiago Castilho de Mello

Communications in Mathematics (2021)

  • Volume: 29, Issue: 2, page 183-186
  • ISSN: 1804-1388

Abstract

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We describe the images of multilinear polynomials of arbitrary degree evaluated on the 3 × 3 upper triangular matrix algebra over an infinite field.

How to cite

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Mello, Thiago Castilho de. "The image of multilinear polynomials evaluated on $3\times 3$ upper triangular matrices." Communications in Mathematics 29.2 (2021): 183-186. <http://eudml.org/doc/297566>.

@article{Mello2021,
abstract = {We describe the images of multilinear polynomials of arbitrary degree evaluated on the $3\times 3$ upper triangular matrix algebra over an infinite field.},
author = {Mello, Thiago Castilho de},
journal = {Communications in Mathematics},
keywords = {multilinear polynomials; upper triangular matrices; Lvov-Kaplansky's conjecture},
language = {eng},
number = {2},
pages = {183-186},
publisher = {University of Ostrava},
title = {The image of multilinear polynomials evaluated on $3\times 3$ upper triangular matrices},
url = {http://eudml.org/doc/297566},
volume = {29},
year = {2021},
}

TY - JOUR
AU - Mello, Thiago Castilho de
TI - The image of multilinear polynomials evaluated on $3\times 3$ upper triangular matrices
JO - Communications in Mathematics
PY - 2021
PB - University of Ostrava
VL - 29
IS - 2
SP - 183
EP - 186
AB - We describe the images of multilinear polynomials of arbitrary degree evaluated on the $3\times 3$ upper triangular matrix algebra over an infinite field.
LA - eng
KW - multilinear polynomials; upper triangular matrices; Lvov-Kaplansky's conjecture
UR - http://eudml.org/doc/297566
ER -

References

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  4. Fagundes, P.S., Mello, T.C. de, 10.7153/oam-2019-13-18, Oper. Matrices, 13, 1, 2019, 283-292, (2019) DOI10.7153/oam-2019-13-18
  5. Filippov, V.T., Kharchenko, V.K., Shestakov, I.P., 10.1201/9781420003451.axb, 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. (2006) DOI10.1201/9781420003451.axb
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  7. Kanel-Belov, A., Malev, S., Rowen, L., 10.1090/proc/12478, Proc. Amer. Math. Soc., 144, 2016, 7-19, (2016) DOI10.1090/proc/12478
  8. Kanel-Belov, A., Malev, S., Rowen, L., Evaluations of Noncommutative Polynomials on Finite Dimensional Algebras. L2’vov-Kaplansky Conjecture, SIGMA, 16, 2020, 61 pp, (2020) 
  9. Malev, A., The image of non-commutative polynomials evaluated on 2 × 2 matrices over an arbitrary field, J. Algebra Appl., 13, 6, 2014, 12 pp, (2014) 
  10. Wang, Y., 10.1080/03081087.2019.1614519, Linear and Multilinear Algebra, 67, 11, 2019, 2366-2372, (2019) DOI10.1080/03081087.2019.1614519
  11. Wang, Y., Liu, P., Bai, J., The images of multilinear polynomials on 2 × 2 upper triangular matrix algebras (Correction), Linear and Multilinear Algebra, 67, 11, 2019, i-vi, (2019) 

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