Grupos de Trabajo
Reading Groupoid - Lie algebroid connections, representations and cohomology
Ponente: Oscar Carballal (UCM)Fecha: martes 24 de febrero de 2026 - 15:30Lugar: Aula Gris 2, ICMAT
Online: https://us02web.zoom.us/j/83154047051?pwd=hLgYMgeEaXl7sm6yDbGbrux9jAOepl.1 (ID: 831 5404 7051; Código de acceso: 050861)
Resumen:
One of the early glimpses of Lie algebroid connections can be traced back to Poisson geometry, when Izu Vaisman, in his study of the geometric quantisation of Poisson manifolds, introduced the notion of contravariant derivatives. This framework was subsequently developed by Rui Loja Fernandes, who employed it to study global properties of Poisson manifolds and later extended the construction to the broader setting of Lie algebroids.
In this talk, we shall introduce the notion of a Lie algebroid connection on a vector bundle. We will also discuss representations of Lie algebroids (namely, flat Lie algebroid connections) and Lie algebroid cohomology, establishing the one-to-one correspondence between Lie algebroid representations and degree +1 graded derivations of the associated exterior algebra that are coboundary operators.
Finally, we shall explain how this framework naturally gives rise to parallel transport along A-paths, thereby enabling the comparison of points along different orbits of a Lie algebroid. The theory will be illustrated through several examples.
