Specht property and graded polynomial identities for some non-associative algebras

• Grant number: 24/01338-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2024
• End date: July 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Ivan Chestakov
• Grantee: Daniela Martinez Correa
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 18/23690-6 - Structures, representations, and applications of algebraic systems, AP.TEM

Abstract

This project has the following goals: describe the graded polynomial identities of some non-associative algebras and study the Specht property of the varieties genarated by these graded algebras.Consider $G$ a finite group and $F$ infinite field. The project can be divided in three problemsa) Describe the $G$-graded identities of the Lie algebra of $3\times 3$ upper triangular matrizes over $F$ and study the Specht property of the varieties generated by this graded algebra.b) Study the Spech property of the variety generated by the Lie algebra of $2\times 2$ traceless matrices over $F$, with each of its non-tivial gradings.c) Describe the $\mathbb{Z}_2$-identities and the superidentities of the Kaplansky's Jordan simple superalgebra.