Graded polynomial identities and identity with trace, and invariant theory

• Grant number: 19/12498-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: April 01, 2020
• End date: 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

(10)

(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; GUIMARAES, ALAN; KOSHLUKOV, PLAMEN. A note on Z-gradings on the Grassmann algebra and elementary number theory. LINEAR & MULTILINEAR ALGEBRA, v. N/A, p. 21-pg., 2022-04-07. (18/23690-6, 19/12498-0)

FIDELIS, CLAUDEMIR. Graded identities of M-n(E) and their generalizations over infinite fields. Linear Algebra and its Applications, v. 643, p. 23-pg., 2022-03-07. (19/12498-0)

FIDELIS, CLAUDEMIR. Z-graded identities on the infinite-dimensional Grassmann algebra and arithmetic tools: revisited. TURKISH JOURNAL OF MATHEMATICS, v. 46, n. 5, p. 15-pg., 2022-01-01. (19/12498-0)

FIDELIS, CLAUDEMIR. Z-graded identities on the infinite-dimensional Grassmann algebra and arithmetic tools: revisited. TURKISH JOURNAL OF MATHEMATICS, v. N/A, p. 14-pg., 2022-03-09. (19/12498-0)

GUIMARAES, ALAN; FIDELIS, CLAUDEMIR; DIAS, LAISE. Z(q)-graded identities and central polynomials of the Grassmann algebra. Linear Algebra and its Applications, v. 609, p. 25-pg., 2021-01-15. (19/12498-0)

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)

FIDELIS, CLAUDEMIR; KOSHLUKOV, PLAMEN; MACEDO, DAVID. Graded identities for Kac-Moody and Heisenberg algebras with the Cartan grading. Linear Algebra and its Applications, v. 638, p. 23-pg., 2022-04-01. (18/23690-6, 19/12498-0)

BRANDAO, ANTONIO; FIDELIS, CLAUDEMIR; GUIMARAES, ALAN. Z-gradings of full support on the Grassmann algebra. Journal of Algebra, v. 601, p. 22-pg., 2022-07-01. (19/12498-0)

FIDELIS, CLAUDEMIR; KOSHLUKOV, PLAMEN. Z-graded identities of the Lie algebras U-1 in characteristic 2. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, v. 174, n. 1, p. 10-pg., 2022-03-08. (19/12498-0, 18/23690-6)