PI-ALGEBRAS, FUNDAMENTAL ALGEBRAS AND APPLICATIONS

• Grant number: 22/15567-5
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: March 04, 2023
• End date: April 10, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Francisco Cesar Polcino Milies
• Grantee: Francisco Cesar Polcino Milies
• Visiting researcher: Antonino Giambruno
• Visiting researcher institution: Università degli Studi di Palermo (UNIPA), Italy
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 20/16594-0 - Non commutative rings and applications, AP.TEM

Abstract

VISIT OF ANTONINO GIAMBRUNO04.03.2023 - 04.05.2023SUMMARYWe shall focus on problems regarding the study of the so-called fundamentalalgebras. These were introduced by Kemer and played a prominent role is in thetheory of varieties of algebras. In a previous joint work, these algebras were used asa tool for the computation of a common polynomial factor in the functions givingthe upper and lower bound of the growth of codimensions. We expect to developan analogous theory in the setting of algebras graded by a finite group G.Also, a notion of central codimension and of central exponent can be definedfor a PI-algebra (considering multilinear polinomials that are central for the givenalgebra). We shall consider the problem of classifying T-ideals having the same PIexponent but different proper central exponent (AU)