Mathematics - 2017-07-08 (page 6 of 6)

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nigel

23:13

Can someone tell me an example of a real semisimple non-split Lie algebra? non-split = no Cartan subalgebra in which each ad(X) is diagonalizable

Typhon

hello

@Daminark (Damint! I was going to read that post!)

Akiva Weinberger

23:47

@Daminark [DATA EXPUNGED]

Kasmir Khaan

hello guys

I have a question on pigeon hole principle , i would be very happy if someone can explain it to me

prove that if 101 integers are selected from the set S = {1,2,3 .......,200} ,then there are two integers such that one divides the other

Akiva Weinberger

Oh!

Hint: Not only will one divide another, but you can always find one that's exactly half another!

Daminark

@KasmirKhaan well, what you need in order to apply pigeonhole?

Akiva Weinberger

Also, if there are 101 things chosen, you presumably want 100 pigeonholes

Kasmir Khaan

hmm

let me show you my idea and tell me if its good

each integer in S can be written in this form

Ted Shifrin

23:54

hi DogAteMy, Demonark, @Kasmir

Kasmir Khaan

x that belongs to the set S = y*2^n where gcd (2,y) =1

@TedShifrin Hello !! :D

Akiva Weinberger

Hi @TedShifrin

Ted Shifrin

Oh, you guys are doing my favorite induction problem. But you're doing it a different way.

Akiva Weinberger

There is too much onion vapor in my eyes

Kasmir Khaan

so by that principle we have the set |B| =100 ( all odd numbers )

Ted Shifrin

23:55

removes DogAteMy's eyes

Akiva Weinberger

aaaaAAAAAAH

Kasmir Khaan

Ted! tell us the good way =p

nigel

Q: non-split real Lie algebra

What are some examples of simple or semisimple non-split real Lie algebras? By non-split, I mean that no Cartan subalgebra $\mathfrak{h}$ is such that $\mathrm{ad}(X)$ is diagonalizable for each $X \in \mathfrak{h}$. Is there a list somewhere? Or how can non-splitness be detected?

lie-algebras

Ted Shifrin

you're doing it the clever way. But I always assigned this as an induction problem when I taught modern algebra (or Spivak).

Akiva Weinberger

(Which should I learn first, Lie algebras or Truth algebras)

LegionMammal978

23:56

You know, sometimes I hope to someday understand some of the discussions which go on in this room

Ted Shifrin

Me too, @LegionMammal978.

Kasmir Khaan

@TedShifrin thanks :D first complement from you to me _ , ehm, well now am stuck with the reasning, can I say that since am gonna pick 101 integers am garateed that a= y *2^n divides b = y*2^m if m>n or otherwise if n>m ?

Ted Shifrin

How many $y$'s can there be?

Kasmir Khaan

100

the odd integers

Ted Shifrin

Hmm ...

Now reread your question.

Daminark

23:59

Hey @Ted!

Kasmir Khaan