Cocharacters and gradedGelfand-Kirillov dimension for PI-algebras
Images of polynomials on superalgebras and commutators on algebras
Specht property and graded polynomial identities for some non-associative algebras
| Full text | |
| Author(s): |
Gargate, Ivan Gonzales
;
de Mello, Thiago Castilho
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Israel Journal of Mathematics; v. 252, n. 1, p. 18-pg., 2022-09-09. |
| Abstract | |
In this paper we prove that the image of multilinear polynomials evaluated on the algebra UTn(K) of n x n upper triangular matrices over an infinite field K equals J(r), a power of its Jacobson ideal J = J(UTn(K)). In particular, this shows that the analogue of the Lvov-Kaplansky conjecture for UTn(K) is true, solving a conjecture of Fagundes and de Mello. To prove that fact, we introduce the notion of commutator-degree of a polynomial and characterize the multilinear polynomials of commutator-degree r in terms of its coefficients. It turns out that the image of a multilinear polynomial f on UTn(K) is J(r) if and only if f has commutator-degree r. (AU) | |
| FAPESP's process: | 18/15627-2 - Gradings, automorphisms and identities in algebras |
| Grantee: | Thiago Castilho de Mello |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 18/23690-6 - Structures, representations, and applications of algebraic systems |
| Grantee: | Ivan Chestakov |
| Support Opportunities: | Research Projects - Thematic Grants |