Zulip Chat Archive

Stream: maths

Topic: lie theory


view this post on Zulip Johan Commelin (Jan 21 2020 at 08:55):

@Oliver Nash I've been following your Lie PRs with curiosity, and I'm a big fan. Could you share in a couple of lines what kind of things you would like to aim for. E.g., may we dream of working towards the classification of semisimple Lie algebras?

view this post on Zulip Oliver Nash (Jan 21 2020 at 20:14):

Thanks @Johan Commelin I'm very grateful for the numerous very helpful improvements that you and others have provided. I do have the semi-simple classification in mind but I've been telling myself just to aim for the statement for now, rather than the proof.

view this post on Zulip Johan Commelin (Jan 21 2020 at 20:15):

Even the statement would be cool!

view this post on Zulip Oliver Nash (Jan 21 2020 at 20:15):

I hope so :)

view this post on Zulip Oliver Nash (Jan 21 2020 at 20:16):

I'm a differential geometer at heart though and I'd really like to define the Lie algebra structure on vector fields of a smooth manifold since IMHO until we have that, the tangent bundle is just another vector bundle but once we have that, we're really doing differential geometry.

view this post on Zulip Oliver Nash (Jan 21 2020 at 20:16):

(Obviously this doesn't really need any Lie theory.)

view this post on Zulip Oliver Nash (Jan 21 2020 at 20:17):

I actually tried this a week or two ago but I learned that there was a moderate amount of work to do even to prove that the continuous/smooth sections of the tangent bundle are an additive group, and that most of this should be done for vector bundles (not yet defined) so I backed off for the time being.

view this post on Zulip Oliver Nash (Jan 21 2020 at 20:18):

So for now I'll probably just keep plugging away trying to get to the statement of the classification. I looked for the trace because I was thinking I should be able to state Cartan's criterion for semisimplicity etc.

view this post on Zulip Oliver Nash (Jan 21 2020 at 20:19):

Unfortunately (for now) my day job takes up far more of my time than I'd like so my progress has been somewhat glacial but nevertheless, non-zero!

view this post on Zulip Johan Commelin (Jan 21 2020 at 20:20):

I really appreciate what you've done so far.

view this post on Zulip Oliver Nash (Jan 21 2020 at 20:20):

Not at all, most fun I've had in years!

view this post on Zulip Oliver Nash (Jan 21 2020 at 20:21):

Well, perhaps I exaggerate, but I do enjoy it!

view this post on Zulip Kevin Buzzard (Jan 21 2020 at 21:59):

I know the feeling. It's an open source project and people contribute when they have time. Thanks a lot!


Last updated: May 06 2021 at 18:20 UTC