Introduction to algebras with polynomial identities

• Grant number: 16/07173-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): June 01, 2016
• Effective date (End): December 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Humberto Luiz Talpo
• Grantee: Fernando Sônego de Toledo
• 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, and therefore they have been attracting the attention of the algebraist. A polynomial identity of an algebra A is a polynomial f(x1,...,xn) in noncommutative variables such that f(a1,...,an)=0 in A for all a1,...,an in A. If there exist f(x1,...,xn) nonzero we say that A is a PI-algebra. Some examples of PI-algebras: Commutative algebras, finite dimensional algebras and nilpotent algebras. In this work we will study some algebras with polynomial identities, in particular the matrix algebra.