Lie theory reference

[mjo22]

Hello! I have been using jaxlie for a project. It is a great package, thank you for writing it! I’d like to understand the theory better in jaxlie.manifold. Could you link a reference for this? In my problem, I am imaging some 3D model and I would like to use autograd to find the correct rigid body rotation of the model that generated the data.

[brentyi]

Hi, thanks for the nice words!

I unfortunately don't have a single definitive reference to provide; given how universal some of the underlying ideas are, there are also unfortunately a lot of overloaded + redundant terms for the same things.

But here are some resources I like!

• This GTSAM blog post discusses optimization on manifolds specifically for common Lie groups: https://gtsam.org/2021/02/23/uncertainties-part2.html
• Ethan Eade has some very nice writeups: https://ethaneade.com/; the "Gauss-Newton Optimization" document has a "Parameter Perturbations" section that's very relevant.
• The micro Lie paper is comprehensive, although as a result can be dense + intimidating to me: https://arxiv.org/abs/1812.01537

[mjo22]

Thank you for sending these references! This is very helpful.