You don't need to be afraid of Lie algebras!

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[jawadibrahim]

I believe a beginner's experience of Lie Algebra existed in my Quantum Mechanics class I took a while back

[luckyluckydog]

my dream is a full course on group theory for physics (group representations, crystallographic groups, Poincare group and more)

[tomkerruish]

I think the scary part is trying to write in Fraktur.

[baronvonbeandip]

Lie algebras are one of those things that make me want to rush through every book imaginable to understand them. I dunno what it is about that idea that's so damn appealing.

[SerbAtheist]

What about the Lie Algebra with the trivial bracket (product is always 0)?

[josephmellor]

Who else wants to see a Michael Penn/Math Major playlist on Lie Algebras?

[DavidVonR]

The cross product is a Lie algebra? Wow, I didn't know that.

[Iamfafafel]

I just never understood why I should care. and this is speaking as a geometer

[soccergalsara]

i really like your diff form playlist, would you do one on lie algebras ? :D

[Suprdud]

I've been using Lie algebras a lot in Robotics and Dynamics. Learning SE3 was far more simple to me than dual quaternions or screw theory.

[namesurname]

The definition of a lie algebra its not the tangent vector soace ro the identity element of a manifold that it is also a group?

[vokuheila]

Cross product is scary to me so this doesn't help 😂

[natepolidoro]

Thanks to you, Dr. Penn, these concepts have become less intimidating for so many students, including myself.

[shanathered]

yeah, I agree. Lie Algebras are quite tame by comparison to some of the other weirdness that comes up in later courses.

[TechSY]

So that title is a lie





Sorry, I'll see myself out

[tylercrowley]

Is [A, B] = -[B, A] a sufficient condition on the bracket product for it to be a Lie algebra!

[jamesfrancese]

There’s a very good reason the cross product is a Lie bracket: it captures the “micro-geometry” of SO(3), the [Lie] group of volume-preserving rotations, acting on R^3. That’s also why the cross-product relies on a choice of orientation i.e. right-hand rule — you’re computing “instantaneous rotations” of shapes along a fixed axis. (Torque anyone?) The reason this only works in R^3 is that given two vectors (the Lie bracket is a binary operation) there is a unique vector orthogonal to them up to a choice of orientation. Because SO(3) is volume-preserving, it doesn’t reverse directions of normal vectors. [Btw, the reason “volume” and “orientation” are related like this in vector spaces is due to the volume form being a “pseudoscalar”]