REU Meeting - 2026-07-29

This following is a brief summary of our research meeting on 2026-07-29.

Meeting summary

We talked about the Lie functor, which on objects takes each Lie group $G$ and maps it its Lie algebra $\mathfrak{g}$, which is the tangent space at the identity element of $G$. This functor has nice properties, such as preserving products. Lie's Third Theorem says that it's essentially surjective.

We also went over the adjoint representation and a little bit about Tannaka-Krein duality.

Tasks for next meeting

Coming soon!

(For now, focus on typesetting the stuff we've learned so far.)

References

nLab