T. C. de Mello

activity

20122026

most citedImages of multilinear polynomials on

n \times n

upper triangular matrices over infinite fields

22 citations · 92 across the 19 of their papers we have counts for

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20 papers · 1 filter

math.RA2026

Generalized Commutator on Octonion Algebra

Thiago Castilho De Mello, Prachi Saini

Let $O$ be an octonion algebra over a field $F$ of characteristic different from $2$ , and let $A, B \in O$ , not both zero. We study the image of the generalized comm…

math.RA2026

Images of polynomials with involution on $2 \times 2$ matrices

Lucio Centrone, Thiago Castilho de Mello

Let $F$ be a field and let $M_{2} (F)$ be the algebra of $2 \times 2$ matrices endowed with an involution of the first kind. We study the image of multilinear $*$ -pol…

math.RA2023★ 1 cited

Polynomial identities and images of polynomials on null-filiform Leibniz algebras

Thiago Castilho de Mello, Manuela da Silva Souza

In this paper we study identities and images of polynomials on null-filiform Leibniz algebras. If $L_{n}$ is an $n$ -dimensional null-filiform Leibniz algebra, we exhibit a finite min…

math.RA2022★ 3 cited

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…

math.RA2022★ 5 cited

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 $M_{n} (K)$ over a field $K$ endowed with its cano…

math.RA2021★ 6 cited

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 $f$ evaluated on $n \times n$ matrices is a vector space. A weaker version of this conject…

math.RA2021★ 5 cited

Homogeneous involutions on upper triangular matrices

Thiago Castilho de Mello

Let $K$ be a field of characteristic different from 2 and let $G$ be a group. If the algebra $U T_{n}$ of $n \times n$ upper triangular matrices over $K$ is endowed with a $G$ -grading…

math.RA2021★ 22 cited

Images of multilinear polynomials on $n \times n$ 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 $U T_{n} (K)$ of $n \times n$ upper triangular matrices over an infinite field $K$ equals $J^{r}$ …

math.RA2020

Relatively free algebras of finite rank

Thiago Castilho de Mello, Felipe Yukihide Yasumura

Let $K$ be a field of characteristic zero and $B = B_{0} + B_{1}$ a finite dimensional associative superalgebra. In this paper we investigate the polynomial identities of the rela…

math.RA2020

Graded monomial identities and almost non-degenerate gradings on matrices

Lucio Centrone, Diogo Diniz, Thiago Castilho de Mello

Let $F$ be a field of characteristic zero, $G$ be a group and $R$ be the algebra $M_{n} (F)$ with a $G$ -grading. Bahturin and Drensky proved that if $R$ is an elementary and the neutr…

math.RA2019★ 8 cited

The image of multilinear polynomials evaluated on $3 \times 3$ upper triangular matrices

Thiago Castilho de Mello

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

math.RA2017★ 5 cited

Graded Polynomial Identities for Matrices with the Transpose Involution over an Infinite Field

Luís Felipe Gonçalves Fonseca, Thiago Castilho de Mello

Let $F$ be an infinite field, and let $M_{n} (F)$ be the algebra of $n \times n$ matrices over $F$ . Suppose that this algebra is equipped with an elementary grading whose neutral com…

math.RA2016★ 6 cited

Degree-inverting involutions on matrix algebras

Luís Felipe Gonçalves Fonseca, Thiago Castilho de Mello

Let $F$ be an algebraically closed field of characteristic zero, and $G$ be a finite abelian group. If $A = \oplus_{g \in G} A_{g}$ is a $G$ -graded algebra, we study degree-inverting in…

math.RA2016★ 2 cited

Automorphisms of Ideals of Polynomial Rings

Tiago Macedo, Thiago Castilho de Mello

Let $R$ be a commutative integral domain with unit, $f$ be a nonconstant monic polynomial in $R [t]$ , and $I_{f} \subset R [t]$ be the ideal generated by $f$ . In this paper we study th…

math.RA2015★ 10 cited

Graded identities of block-triangular matrices

Diogo Diniz Pereira da Silva e Silva, Thiago Castilho de Mello

Let $F$ be an infinite field and $U T (d_{1}, \dots, d_{n})$ be the algebra of upper block-triangular matrices over $F$ . In this paper we describe a basis for the $G$ -graded polynomial id…

math.RA2014★ 1 cited

Minimal Varieties and Identities of Relatively Free Algebras

Dimas José Gonçalves, Thiago Castilho de Mello

Let $K$ be a field of characteristic zero and let $M_{5}$ be the variety of associative algebras over $K$ , defined by the identity $[x_{1}, x_{2}] [x_{3}, x_{4}, x_{5}]$ . It is well-kno…

math.RA2013★ 6 cited

On graded identities of block-triangular matrices with the grading of Di Vincenzo-Vasilovsky

Thiago Castilho de Mello, Lucio Centrone

The algebra of $n \times n$ matrices over a field $F$ has a natural $Z_{n}$ -grading. Its graded identities have been described by Vasilovsky who extended a previous work of D…

math.RA2012★ 3 cited

A model for the relatively free graded algebra of block triangular matrices with entries from a graded algebra

Thiago Castilho de Mello, Lucio Centrone

Let G be a group and A be a G-graded algebra satisfying a polynomial identity. We buid up a model for the relative free G-graded algebra and we obtain, as an application, the "fact…

math.RA2012★ 4 cited

On the polynomial identities of the algebra $M_{11} (E)$

Thiago Castilho de Mello, Plamen Koshlukov

Verbally prime algebras are important in PI theory. They were described by Kemer over a field $K$ of characteristic zero: 0 and $K < T >$ (the trivial ones), $M_{n} (K)$ , $M_{n} (E)$ , $M_{a…

math.RA2012★ 5 cited

The centre of generic algebras of small PI algebras