| Full text | |
| Author(s): |
Fagundes, Pedro Souza
;
de Mello, Thiago Castilho
;
dos Santos, Pedro Henrique da Silva
Total Authors: 3
|
| Document type: | Journal article |
| Source: | TURKISH JOURNAL OF MATHEMATICS; v. 46, n. 5, p. 16-pg., 2022-01-01. |
| Abstract | |
The well-known Lvov-Kaplansky conjecture states that the image of a multilinear polynomial f evaluated on n x n matrices is a vector space. A weaker version of this conjecture, known as the Mesyan conjecture, states that if m = deg f and n >= m - 1 then its image contains the set of trace zero matrices. Such conjecture has been proved for polynomials of degree m <= 4. The proof of the case m = 4 contains an error in one of the lemmas. In this paper, we correct the proof of such lemma and present some evidence which allows us to state the Mesyan conjecture for the new bound n >= m+1/2 , which cannot be improved. (AU) | |
| FAPESP's process: | 16/09496-7 - The Lvov-Kaplansky conjecture |
| Grantee: | Pedro Souza Fagundes |
| Support Opportunities: | Scholarships in Brazil - Master |
| FAPESP's process: | 19/16994-1 - Algebras that are sums of two PI subalgebras |
| Grantee: | Pedro Souza Fagundes |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 18/23690-6 - Structures, representations, and applications of algebraic systems |
| Grantee: | Ivan Chestakov |
| Support Opportunities: | Research Projects - Thematic Grants |