Lie algebras: isomorphisms and actions

• Grant number: 19/08659-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2019
• End date: September 30, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Mikhailo Dokuchaev
• Grantee: Jose Luis Vilca Rodriguez
• 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

The project will be dedicated to the study of isomorphisms and actions which involve Lie algebras. Our first goal is to give a contribution to the isomorphism problem for universalenveloping algebras of finite-dimensional Lie algebras. The main expected result is to show that this problem has a positive solution in the class of solvable Lie algebras of dimension four over fields of prime characteristic. In the case of not being able to decide completely the isomorphism problem, we are going to look for a counterexample using the GAP (Groups, Algorithms and Programming). Our second goal is to study partial actions of groups on Lie algebras and, eventually, partial actions ofLie groups and Lie algebras on differentiable manifolds. In particular, we are going to develop a Galois theory of partial actions for Lie algebras, extending some recent results of A. L. Agore e G. Militaru.

Scientific publications

(6)

(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)

VILCA RODRIGUEZ, JOSE L.; BRANDAO, TAUAN L. A.; BATISTA, VICTOR M. O.. Principal angles and pairs of totally geodesic submanifolds of the real hyperbolic space. LINEAR & MULTILINEAR ALGEBRA, v. 70, n. 20, p. 16-pg., 2021-06-12. (19/08659-8)

VILCA RODRIGUEZ, JOSE L.. artial actions on reductive Lie algebra. COMMUNICATIONS IN ALGEBRA, v. 50, n. 4, OCT 2021. (19/08659-8)

RODRIGUEZ, JOSE L. VILCA; CORTES, WAGNER. Globalizations of partial group actions on non-associative algebras. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. N/A, p. 24-pg., 2023-05-25. (19/08659-8)

VILCA RODRIGUEZ, JOSE L.; BRANDAO, TAUAN L. A.; BATISTA, VICTOR M. O.. Principal angles and pairs of totally geodesic submanifolds of the real hyperbolic space. LINEAR & MULTILINEAR ALGEBRA, JUN 2021. (19/08659-8)

RODRIGUEZ, JOSE L. VILCA; SCHNEIDER, CSABA; USEFI, HAMID. The isomorphism problem for universal enveloping algebras of solvable Lie algebras. Journal of Algebra, v. 603, p. 26-pg., 2022-08-01. (19/08659-8)

RODRIGUEZ, JOSE L. VILCA; BRANDAO, TAUAN L. A.; BATISTA, VICTOR M. O.. Principal angles in pseudo-euclidean spaces of index 1. LINEAR & MULTILINEAR ALGEBRA, v. N/A, p. 25-pg., 2023-01-10. (19/08659-8)