Evaluations of Polynomials in Algebras: Images, Identities, Gradings and Connectio...
Images of polynomials on algebras with additional structures
| Full text | |
| Author(s): |
Centrone, Lucio
;
de Mello, Thiago Castilho
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Journal of Algebra; v. 614, p. 20-pg., 2023-01-15. |
| Abstract | |
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) | |
| FAPESP's process: | 18/23690-6 - Structures, representations, and applications of algebraic systems |
| Grantee: | Ivan Chestakov |
| Support Opportunities: | Research Projects - Thematic Grants |