Images of graded polynomials on matrix algebras

Autor(es)

Centrone, Lucio ; de Mello, Thiago Castilho

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 614, p. 20-pg., 2023-01-15.

Resumo

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 Mn(K) over a field K endowed with its canonical Zn- grading (Vasilovsky's grading). We explicitly determine the possibilities for the linear span of the image of a multilinear graded polynomial over the field Q of rational numbers and state an analogue of the L'vov-Kaplansky conjecture about images of multilinear graded polynomials on n x n matrices, where n is a prime number. We confirm such conjecture for polynomials of degree 2 over Mn(K) when K is a quadratically closed field of characteristic zero or greater than n and for polynomials of arbitrary degree over matrices of order 2. We also determine all the possible images of semi-homogeneous graded polynomials evaluated on M2(K). (c) 2022 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 18/23690-6 - Estruturas, representações e aplicações de sistemas algébricos
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático