Introduction to algebras with polynomial identities

• Grant number: 24/10457-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: November 01, 2024
• End date: October 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Humberto Luiz Talpo
• Grantee: João Pedro Oliveira Martins
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

The algebras that satisfy polynomial identities (so-called PI-algebras) form an important class of algebras. A polynomial identity of an algebra A is a polynomial f(x1, . . . , xn), in noncommutative variables, which vanishes when evaluated in any elements of A. We say that A is a PI-algebra when there are a non zero polynomial under these conditions. As examples we can mention commutative algebras, finite-dimensional algebras and nilpotent algebras. Considering that polynomial identities say a lot about the structure of an algebra, their study is of great interest, and the main object of study of this project.