On LA-Courant algebroids and their Lie theory

• Grant number: 25/10946-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2025
• End date: September 30, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Cristián Andrés Ortiz González
• Grantee: Ana Carolina de Carvalho Mancur
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this project, we explore the integration/differentiation between Courant double structures known as LA-Courant algebroids and CA-groupoids. The first research line investigates Courant double structures given by Drinfeld doubles of quasi-Lie bialgebroids over Lie groupoids/algebroids, developing their Lie theory. The second line aims to provide a more manageable characterization of LA-Courant algebroids, which are highly non-trivial and challenging to work with, by describing them in terms of Weil algebras. This Weil algebra perspective enables the application of Van Est theory to address the central problem of integrating/differentiating Courant double structures. (AU)