Lie Algebras 5 -- solvable and nilpotent algebras

[@chamirngandjia1198]

Nice video. In case somebody is interested : 1) The converse of Proposition in 12:16 is actually also true, just take I_n to be L^(n). 2) Also, the statement of proposition of 17:46 is an equivalence. 3) Also, the statement of proposition of 23:49 is an equivalence.

[@araamdaher5994]

I would like to suggest doing a course on representation theory as a next project. Apart from that, thank you for your effort, I very much benefit from these videos!

[@Juniper-111]

Thanks for doing this! Currently in a class on lie algebras (which is going a bit faster than the series). Excited for you to talk about the finite simple representations of sl_2! (and for representation theory of lie algebras in general because I find those ideas kinda complicated)

[@krisbrandenberger544]

@ 14:09 The I_1 and I_2 should be reversed.

[@gabr1vp]

I would like to suggest you to have a pdf companion to this series! it's nice to see the proofs step by step explained by you, but I also think it would be nice to have the collection of all theorems, corollaries and definitions in a single pdf file. So we could sweep our eyes through whenever we don't remember the definition of something or what has been already proven. It can also give us a bigger picture of things and serve as offline study material for those that prefer to read things. Cheers!

[@vector8310]

Call me a geek but I was smitten by the proposition that L/I is abelian iff L' is in I. Lie algebras are fascinating.

[@robshaw2639]

I was also anticipating a course on Galois Theory - did Michael not get the green light to teach that course?

[@yoyostutoring]

"Let's supoose that L mod I is abeal"

[@edheakes2663]

I was initially struggling to understand the weight function. Then it clicked that it is a form of choice function. For each a belonging to A, lambda chooses an eigenvalue of a. Does this make sense?

[@LuFreitas0000]

loving the lectures series! On the HW at 35:00 I don't get why write the algebra as L^n+Z(L) mod Z(L), for me this quotient is the same as simply L^n/Z(L)

[@milenamarquez]

That part confused me a lot, too. But L^n may not include the entire Z(L), in which case you can't mod out the space by Z(L). You must add Z(L) first to make it a null space.

[@mrl9418]

Exercise 4 is doable, but i think it needs char(F) different from 2, otherwise the Lie algebra isn't semisimple either

[@youssefelnaggar5216]

There's no audio

[@wertibl3]

Must be added now. Working fine on my end.