arXiv subjects

Rafael Bezerra dos Santos

Publications and source records attributed to Rafael Bezerra dos Santos.

4 recordsLinked to original sources

arXiv2026

Polynomial identities, central polynomials and cocharacters of $M_2(F)$ with transpose superinvolution

Let $F$ be a field of characteristic zero and consider $M_2(F),$ the algebra of $2\times 2$ matrices over $F,$ with canonical $\mathbb{Z}_2$-grading and endowed with transpose superinvolution. In this paper, we present the generators of the $T_2^*$-ideal of $*$-identities and of the $T_2^*$-subspace of central $*$-polynomials of $M_2(F).$ As a consequence, we determine the sequences of $*$-codimensions and $\langle n\rangle$-cocharacters of $M_2(F)$. In particular, we prove that the $n$-th $*$-codimension grows like $4^nn^{-1/2}$.

math.RA↗

arXiv2026

Polynomial identities, central polynomials and cocharacters of $M_2(F)$ with $G$-graded involution

Let $F$ be a field of characteristic zero, $G$ be a finite abelian group and $M_2(F)$ be the algebra of $2\times 2$ matrices over $F$. In this paper, we consider all $G$-graded involutions on $M_2(F)$ and determine the generators of the $T_{(G,*)}$-ideal of identities and of the $T_{(G,*)}$-space of central polynomials of $M_2(F)$. Moreover, we explicitly compute the $\langle n\rangle$-cocharacter and the $n$-th $(G, *)$-codimensions for most of the gradings. For the case of gradings by the Klein group, the $(G, *)$-central codimensions and proper central $(G, *)$-codimensions are also explicitly computed.

math.RA↗

arXiv2025

On the colength sequence of algebras with graded involution

In recent years, many results have been established regarding classifications of varieties whose colength sequences are bounded by a fixed constant. In this work, we explore this theme in the setting of algebras endowed with a graded involution, called $(G,*)$-algebras. We give an explicit description of the decomposition of the $\langle n \rangle$-cocharacter for some important $(G,*)$-algebras $A$, for every $\langle n \rangle=(n_1, \ldots, n_{2t})$. For each algebra $A$, the $n$th colength is defined as the number of irreducible components that appear in these decompositions. Our aim is to classify varieties whose $n$th colengths are bounded by a fixed constant.

math.RA↗

arXiv2023

Differential identities and polynomial growth of the codimensions

Let $A$ be an associative algebra over a field $F$ of characteristic zero and let $L$ be a Lie algebra over $F$. If $L$ acts on $A$ by derivations, then such an action determines an action of its universal enveloping algebra $U(L)$ and in this case we refer to $A$ as algebra with derivations or $L$-algebra. Here we give a characterization of the ideal of differential identities of finite dimensional $L$-algebras $A$ in case the corresponding sequence of differential codimensions $c_n^L (A)$, $n\geq 1$, is polynomially bounded. As a consequence, we also characterize $L$-algebras with multiplicities of the differential cocharacter bounded by a constant.

math.RA↗