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Images of graded polynomials on simple algebras

Grant number: 24/04059-4
Support Opportunities:Scholarships abroad - Research Internship - Master's degree
Effective date (Start): August 01, 2024
Effective date (End): January 31, 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
Research place: 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.

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