Algebra Seminar: Lanfranchi -- The Lie Group-Lie Algebra Correspondence in Tangent Categories

Marcello Lanfranchi (Macquarie University) will be speaking in the algebra seminar.  We
will go out for lunch after the talk---all are welcome to join! 

When: 12-1pm Friday September 18 

Where: Carslaw 275 

Title: The Lie Group-Lie Algebra Correspondence in Tangent Categories 

Abstract: Classic Lie theory establishes a correspondence between Lie groups and Lie
algebras.  An analogous correspondence also exists for group objects in affine schemes.
Both smooth manifolds and affine schemes form tangent categories, which provide a
categorical context for differential geometry.  

In this talk, we show how to construct the Lie correspondence entirely from the tangent
structure.  We define Lie groups in a tangent category as group objects that admit the
tangent space at the unit and construct the internal Lie algebra as the representing
object of a certain functor.  Lastly, we show that our construction generalizes the
usual Lie correspondence in both differential and algebraic geometry.  

During the talk, I will give a quick introduction to tangent categories.  

Paper: https://arxiv.org/abs/2609.03449