Classification of Lie algebras endowed with ad-invariant metrics.

• Grant number: 24/03063-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2024
• End date: December 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Viviana Jorgelina Del Barco
• Grantee: Marcos Ricardo Cavicchioli de Almeida
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The present project aims to deepen the student's understanding of the structure of an abstract Lie algebra equipped with an ad-invariant metric. In this regard, the objective is to comprehend the classification of Lie algebras of fixed dimension endowed with this type of function, up to isomorphism. More precisely, the classification will be studied in algebras of dimension up to 4.Additionally, the project will solidify the student's research skills in mathematics by expanding their knowledge of techniques and processes of classification in mathematics.