Graded polynomial identities and identity with trace, and invariant theory

• Grant number: 19/12498-0
• Support Opportunities: Scholarships in Brazil - Post-Doctorate
• Effective date (Start): April 01, 2020
• Effective date (End): November 30, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Ivan Chestakov
• Grantee: Claudemir Fideles Bezerra Júnior
• 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

The main object of study of this research project is the theory of polynomial identities for some important algebras (not necessarily associative). We are interested in algebras endowed with a particular linear map called trace. In the first section we shall give a background concerning the theory of the polynomial identities for algebras. In the second one, which contains the project itself, we shall introduce the algebras with trace and graded algebras; we give a list of concrete problems, their background, and some of the expected results concerning them. In the last section, we shall discuss the methodology of investigation, the time-scale of the project and the potential collaborations. We can also cite the importance of the exchange of experiences between the candidate and the supervisor, in addition it will make it possible to establish new partnerships. We can also mention the complementation of the training of the proponent, who is a recent doctor. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

FIDELIS, CLAUDEMIR; DINIZ, DIOGO; BERNARDO, LEOMAQUES; KOSHLUKOV, PLAMEN. Graded Identities and Central Polynomials for the Verbally Prime Algebras. ALGEBRAS AND REPRESENTATION THEORY, JUL 2021. (19/12498-0, 18/23690-6)

DINIZ, DIOGO; FIDELIS, CLAUDEMIR; KOSHLUKOV, PLAMEN. GRADED IDENTITIES FOR ALGEBRAS WITH ELEMENTARY GRADINGS OVER AN INFINITE FIELD. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, JAN 2022. (18/23690-6, 19/12498-0)