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16 papers · 1 filter
A new approach to the Lvov-Kaplansky conjecture through gradings
Ivan Gonzales Gargate, Thiago Castilho de Mello
In this paper we consider images of (ordinary) noncommutative polynomials on matrix algebras endowed with a graded structure. We give necessary and sufficient conditions to verify…
Images of graded polynomials on matrix algebras
Lucio Centrone, Thiago Castilho de Mello
The aim of this paper is to start the study of images of graded polynomials on full matrix algebras. We work with the matrix algebra over a field endowed with its cano…
The Mesyan Conjecture: a restatement and a correction
Pedro Souza Fagundes, Thiago Castilho de Mello, Pedro Henrique da Silva dos Santos
The well-known Lvov-Kaplansky conjecture states that the image of a multilinear polynomial evaluated on matrices is a vector space. A weaker version of this conject…
Homogeneous involutions on upper triangular matrices
Thiago Castilho de Mello
Let be a field of characteristic different from 2 and let be a group. If the algebra of upper triangular matrices over is endowed with a -grading…
Images of multilinear polynomials on upper triangular matrices over infinite fields
Ivan Gonzales Gargate, Thiago Castilho de Mello
In this paper we prove that the image of multilinear polynomials evaluated on the algebra of upper triangular matrices over an infinite field equals …
Central extensions of 3-dimensional Zinbiel algebras
María Alejandra Alvarez, Thiago Castilho de Mello, Ivan Kaygorodov
We describe all central extensions of all -dimensional non-zero complex Zinbiel algebras. As a corollary, we have a full classification of -dimensional non-trivial complex Zi…