Loops and related algebras

• Grant number: 21/12820-9
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: February 04, 2022
• End date: June 30, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Ivan Chestakov
• Grantee: Ivan Chestakov
• Visiting researcher: Marina Rasskazova
• Visiting researcher institution: Omsk State Technical University (OmSTU), Russia
• 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

In this project we formulate some Conjectures and Problems about Moufang loops, alternative and super Binary-Lie algebras. We hope give significant contribution during this period in solving those Conjectures and Problem. In particular, we hope to obtain important results in the following directions: 1) Commutative Moufang loops and alternative algebras (calculate the order of free loop with $7$ and $8$ generators). 2) Super Binary-Lie algebras (classify simple algebras with abelian even part). 3) Malcev algebras and its alternative envelops (prove the speciality of some Malcev algebras). 4) Moufang theorem and its generalization (prove this theorem in some non-Moufang varieties). 5) Steiner loops and Rajah's problem (to describe free Steiner loops in some varieties connected with Rajah's problem). 6) Deformations of Coxeter group algebras (classify deformation of some group algebras of Coxeter groups). 7) Free Bol loops (to construct a basis of free Bol loops). 8) Symplectic alternating nilpotent algebras (calculate class of nilpotence of those algebras). 9) Simple Lie algebras over a field of characteristic two (classify toral subalgebras in some simple Lie algebras). (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)

GRISHKOV, A.; RASSKAZOVA, M.; DOS ANJOS, G. SOUZA. Free Bol loops of exponent two. Journal of Algebra, v. 628, p. 17-pg., 2023-04-18. (21/12820-9, 18/23690-6)