Images of polynomials on algebras with additional structures

• Grant number: 22/13058-6
• Support Opportunities: Scholarships in Brazil - Master
• Start date: April 01, 2023
• End date: August 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Thiago Castilho de Mello
• Grantee: Daniela do Nascimento Rodrigues
• Host Institution: Instituto de Ciência e Tecnologia (ICT). Universidade Federal de São Paulo (UNIFESP). Campus São José dos Campos. São José dos Campos , SP, Brazil
• Associated research grant: 18/23690-6 - Structures, representations, and applications of algebraic systems, AP.TEM
• Associated scholarship(s): 24/04059-4 - Images of graded polynomials on simple algebras, BE.EP.MS

Abstract

In this research project we aim to study images of polynomials on algebras with additional structures. More specifically, we will study images of polynomials on matrix algebras endowed with its usual Z-grading. We will try to prove results similar to those already known for the usual grading by the cyclic group of order n.We will focous on multilinear polynomials, trying to prove general or parcial results that motivate conjectures analogous to the Lvov-Kaplansky conjecture, which states that the image of a multilinear polynomial on the matrix algebra of order n is a vector subspace.