Math's greatest Lie!!

We look at a nice construction of one of the most important Lie algebras.

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[michalbotor]

Haha.
My physics professor once hosted a seminar called "Can a physicist count on CUDA?", which in Polish can be also understood as "Can a physicist count on MIRACLES?" and he was much amused when a group of theologians fell for his prank and was shocked to find themselves listen for some reason to very cryptic-sounding general-purpose computing on graphics processing units in molecular dynamics instead. 😂

[yulflip]

I clicked specifically because I was hoping to dive into Lie groups/algebra. Not disappointed. I'd love to see more.

[TheLetterW]

This was a great light introduction to Lie Groups and Lie Algebras. It was clear, and simple. Really enjoyed it. Hope more videos on this subject are made.

[matthewcolquhoun]

"What we're doing here is fairly simple."

LIE




groups

[mattmethod]

Thanks for the glimpse Michael! As an undergrad standing outside the gates of some beautiful but forbidding topics, these kinds of videos are super helpful and exciting!

[JoeWolf]

5 minutes in and I was wondering "When is he going to talk about the big falsehood?" That's what I get for watching these first thing in the morning.

[goodplacetostop]

3:02 G2 Esports
15:02 The cake is a Lie

[Astrophysikus]

This is so brilliant! Lie algebras is one of these topics that felt a little bit overwhelming when I was a young physics student over a decade ago. Now, I work as a software engineer, and while the job pays the bills, I often have the feeling that it is somewhat lacking in the sense that it does not offer any real intellectual challenges. Your videos, on the other hand, bring me a sense of enjoyment of pure learning and understanding that I miss quite a lot these days!

[vincentbutton]

Now I'm having to go back to look at your older videos to understand stuff. Fantastic!

[burpleson]

1) When I saw the title, I assumed this is where you were heading, and 2) Yes, please do more videos on this topic.

[criskity]

5:06 Don't you mean "whose determinant is 1"? (not zero?)

[jacobadamczyk]

@5:13 "Determinant is zero" but ad-bc=1 on the board, should in fact =1 otherwise we can't get the identity matrix! And yes it really is a 3D surface embedded in 4D because of this extra constraint (can think of one of the 4 numbers as being fixed)

[goodplacetostop]

HOMEWORK : Let L be the real vector space R³. Define [x, y] = x × y (cross product of vectors) for x, y ∈ L, and verify that L is a Lie algebra. Write down the structure constants relative to the usual basis of R³.

[meimoscoso]

Looks so interesting, i would love to see more about Lie algebras and Lie groups

[DRposko]

was just about to write an angry comment regarding the clickbait ...

... then I realized the true meaning of the „Lie“ in your title. Now I love it!

[sadface]

I have been wanting to learn about lie groups for a while now.

[unixux]

Fascinating stuff, do more ! Also do more topology !

[jessicawang]

I got clickbaited, then saw the words "lie algebra", and now I'm gonna stay in your channel forever

[steviebudden]

Great video. You had me fooled with the title - I got a different interesting video to the one I was expecting. :)
Small point. At 5:09 you claim that SL_2 is the set of matrices with determinant 0 rather than 1 (as you correctly have written down). One of those slips of the tongue which are so easy to make. It might be nice to mention that in the preface or whatever you call it, the writting above describing the video.

[Muzrikulandulajevon]

Finally! Yep, I would like to see other videos about this topic.