Vector fields on Lie groupoids and its Lie-Rinehart structure 

The aim of this talk is to explore the Lie-Rinehart algebra structure associated with the 2-algebra of multiplicative vector fields on a Lie groupoid. To this end, we will start by examining the Lie-Rinehart structure present on manifolds and Lie algebroids. Next, we will discuss the notions of Lie groupoids and multiplicative vector fields on them, along with some illustrative examples. Finally, we will analyze the Lie-Rinehart structure un- derlying the 2-algebra of multiplicative vector fields. This is joint work with C. Ortiz and J. Waldron.