Classification of Lie algebras and Dynkin diagrams - Lec 14 - Frederic Schuller

This is from a series of lectures - "Lectures on the Geometric Anatomy of Theoretical Physics" delivered by Dr.Frederic P Schuller

[theleastcreative]

Is anyone else having problems with the sound?

[jeanbillie]

I have learned a great deal from this lecture.

At 11:58, If I remember correctly, the Lie bracket of two Lie algebras should be " the linear combination " of elements of these sets.

[tim-cca]

3:06 levi decomposition
18:37 adjoint
21:38 killing form
29:47 structure constants
39:52 Cartan subalgebra
48:43 roots of Lie algebra
1:12:26 weyl transformation
1:27:06 cartan matrix
1:37:02 dynkin diagrams

[luisgeniole]

It looks like a professor, it sounds like a tesla coil

[manjit-]

Marvelous way of communication. How I can watch all lectures on Lie algebra??

[somasundaramsankaranarayan]

At 10:48, there should be an equal to sign on the last line and not a subset sign for the condition of no non trivial ideals to hold

[danschmidt]

If all of this seems hopelessly abstract, do not despair, he spends the entirety of the next two lectures going over everything to date, including this material, as applied to a single example. (It's still pretty abstract, though.)

[jwp]

1:14:44 Shouldn't it be that Weyl group be defined as the group generated by W, not just W? I was confused when I apply his definition to sl(2, C) treated in lecture 16, and the only way to be consistent seems to define Weyl group as the way I mentioned.

[daujok]

Am I the only one watching this great lecture on Lie Algebra? I really enjoys professor Frederic P Schuller's teaching!!

[kenreeb]

I am unsure about 1:31:So for the s_pi_i(pi_i) = -pi_i when i=j ? or = 3pi_i? if it is = -1(if i=j), then there is no constraint that the -2K*(...)/K*(...) to be non-negative (i.e. it can be negative, which violates that epsilon summation epsilon is either +1 or -1 (either positive integers or negative integers) ? May someone help to clarify this, thank you.

[aplund]

I once had one of those thinking about thinking moments.

[Smooth_Manifold]

In 57:58, do we actually choose only the "+"s OR only the "-"s of the roots (witch are linearly independent) so they span H*? Is this the reason why the set Φ is not linearly independent?

[millerfour]

7:15, 14:40, 23:27, 29:24, 34:12, 42:08, 52:00 (why), 56:47, 1:07:39, 1:23:56, 1:30:50, 1:34:12, 1:45:15

[manjit-]

How Levi decomposition is helpful in classification ?

[luthfianurhalimah]

Why is it simpler to use Complex Lie Algebra to study its classification?

[kapoioBCS]

How this definition of the Cartan subalgebra H is related to the more known definition of Cartan subalgebra:

A Cartan subalgebra of a Lie algebra L is a subalgebra H, satisfying the following two conditions:

(i) H is a nilpotent Lie algebra
(ii) N_L(H)=H where N_L(H) is the normalized of H in L

Does anyone knows?

[diegotapias]

Can someone recommend me a book where I can complement this lecture?

[Evan]

1:05:04 when he says "that means this guy is an element of H*" I had to remember that H* is linear combinations of elements in π with complex coefficients, and π is a subset of a set of eigenvalues of the Lie bracket of complex vector spaces, so the elements of π are complex. So it makes sense even though k outputs a complex number.

[manishankarpandeypandey]

Sir, can you tell me which book you are following?

[tomking]

Is this a postgrad course? You’re introducing lots of definitions very quickly, especially at the start where you’re giving definitions within definitions.