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Iritan Ferreira dos Santos

Publications and source records attributed to Iritan Ferreira dos Santos.

3 recordsLinked to original sources
arXiv2026

On multilinear polynomial identities for $2\times2$ matrices in characteristic $2$

Let $K$ be an infinite field of characteristic $2$. It is well known that the Lie algebra $\mathfrak{gl}_2(K)=M_2(K)^{(-)}$ of all $2\times 2$ matrices does not admit a finite basis of polynomial identities. Similarly, the finite basis problem for the associative algebra $M_2(K)$ remains open. In this note, we obtain two multilinear identities of degree $5$ for $M_2(K)$ and prove that, together with the standard polynomial of degree $4$, they generate all multilinear identities of degree up to $7$. Moreover, we prove that none of the three generators can be omitted.

math.RA↗
arXiv2025

Novikov algebras in low dimension: identities, images and codimensions

Polynomial identities of two-dimensional Novikov algebras are studied over the complex field $\mathbb{C}$. We determine minimal generating sets for the T-ideals of the polynomial identities and linear bases for the corresponding relatively free algebras. As a consequence, we establish that polynomial identities separate two-dimensional Novikov algebras, which are not associative. Namely, any two-dimensional Novikov algebras, which are not associative, are isomorphic if and only if they satisfy the same polynomial identities. Moreover, we obtain the codimension sequences of all these algebras. In particular, every two-dimensional Novikov algebra has at most linear growth of its codimension sequence. We explicitly describe multilinear images of every two-dimensional Novikov algebra. In particular, we show that these images are vector spaces.

math.RA↗