| Title:
|
The image of multilinear polynomials evaluated on $3\times 3$ upper triangular matrices (English) |
| Author:
|
Mello, Thiago Castilho de |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
29 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
183-186 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We describe the images of multilinear polynomials of arbitrary degree evaluated on the $3\times 3$ upper triangular matrix algebra over an infinite field. (English) |
| Keyword:
|
multilinear polynomials |
| Keyword:
|
upper triangular matrices |
| Keyword:
|
Lvov-Kaplansky's conjecture |
| MSC:
|
16R10 |
| MSC:
|
16S50 |
| idZBL:
|
Zbl 07426417 |
| idMR:
|
MR4285750 |
| . |
| Date available:
|
2021-11-04T12:11:18Z |
| Last updated:
|
2021-12-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149188 |
| . |
| Reference:
|
[1] Drensky, V.: Free Algebras and PI-Algebras. Graduate course in algebra.2000, Springer-Verlag, |
| Reference:
|
[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. |
| Reference:
|
[3] Fagundes, P. S.: The images of multilinear polynomials on strictly upper triangular matrices.Linear Algebra Appl., 563, 2019, 287-301, 10.1016/j.laa.2018.11.014 |
| Reference:
|
[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, 10.7153/oam-2019-13-18 |
| Reference:
|
[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. 10.1201/9781420003451.axb |
| Reference:
|
[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, 10.1090/S0002-9939-2011-10963-8 |
| Reference:
|
[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, 10.1090/proc/12478 |
| Reference:
|
[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, |
| Reference:
|
[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, |
| Reference:
|
[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, 10.1080/03081087.2019.1614519 |
| Reference:
|
[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, |
| . |
