On maps preserving some identities on nonassociative algebraic structures

• Grant number: 22/02571-4
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: November 01, 2022
• End date: March 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Henrique Guzzo Junior
• Grantee: Douglas de Araujo Smigly
• 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

This research project consists of three lines of investigation on maps defined over associative/non-associative algebraic structures. The first one is to describe some additive maps satisfying mild identities on nonassociative structures namely, alternative rings or algebras.The second part consists in to study the characterization of certain maps on ultra algebras and nonassociative ultra algebras. And the last goal is to study the behavior of derivation type maps on axial algebras, i.e. we would like to determine when a multiplicative derivation is additive on such algebras.

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)

FERREIRA, BRUNO L. M.; SMIGLY, DOUGLAS DE ARAUJO; BARREIRO, ELISABETE. Multiplicative isomorphisms and derivations on axial algebras. Journal of Pure and Applied Algebra, v. 228, n. 12, p. 27-pg., 2024-06-18. (22/02571-4)

FERREIRA, BRUNO LEONARDO MACEDO; BARREIRO, ELISABETE; SMIGLY, DOUGLAS DE ARAUJO. A Hua-type theorem for Cayley algebras. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, v. 73, n. 5, p. 20-pg., 2024-08-01. (22/02571-4)