Images of graded polynomials on simple algebras

• Grant number: 24/04059-4
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: August 28, 2024
• End date: February 27, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Thiago Castilho de Mello
• Grantee: Daniela do Nascimento Rodrigues
• Supervisor: Mikhail Chebotar
• 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
• Institution abroad: Kent State University, United States
• Associated to the scholarship: 22/13058-6 - Images of polynomials on algebras with additional structures, BP.MS

Abstract

The Lvov-Kaplansky conjecture states that the image of a multilinear polynomial on Mn(F) is a vector subspace of Mn(F). In this research project, we aim to study the image of multilinear polynomials on some classes of simple algebras. First we will consider images of graded polynomials on Mn(F) endowed with some types of elementary gradings and second we will consider images of polynomials on Mn(D) where D is a division algebra.