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Root Systems

Anonymous Tue 19 Jan 01:07:02 2021 No.12598692 View Reply Original Report

Quoted By: >>12598735 >>12598739 >>12598833

Besides being used to classify the finite dimensional complex semi-simple Lie algebras, what else are root systems useful for? Are there areas of active research that use root systems?

Anonymous

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Anonymous Tue 19 Jan 2021 01:19:31 No.12598735 Report

Quoted By:

>>12598692
Looks like you have about 1 paper mentioning them a day, so it can't be that bad.

I actually take an interest in Lie algebras over ${\mathbb Q}$ , so I should go back at it.

Anonymous

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Anonymous Tue 19 Jan 2021 01:20:35 No.12598739 Report

Quoted By: >>12598810

>>12598692 (OP)
Looks like you have about 1 paper mentioning them a day, so it can't be that bad.

I actually take an interest in Lie algebras over Q, so I should go back at it

Anonymous

Anonymous Tue 19 Jan 2021 01:44:42 No.12598810 Report

Quoted By:

>>12598739
very interesting. Thank you.

Anonymous

Anonymous Tue 19 Jan 2021 01:51:38 No.12598824 Report

Quoted By: >>12600156

how is this any different than the nth roots of 1?

Anonymous

Anonymous Tue 19 Jan 2021 01:54:52 No.12598833 Report

Quoted By: >>12598895

>>12598692
What happened to a-b and -a+b?

Anonymous

Anonymous Tue 19 Jan 2021 02:13:01 No.12598895 Report

Quoted By:

>>12598833
if you only added a-b and -a+b to the set of vectors in the original post, then the set would fail to be a root system. Indeed, the reflection of -a+b along the hyperplane perpendicular to a would fail to be an element of the set, which would contradict the third axiom of a root system.

Anonymous

Anonymous Tue 19 Jan 2021 12:03:45 No.12600156 Report

Quoted By: >>12600289

>>12598824
this is the dumbest post I have ever seen here

Anonymous

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Anonymous Tue 19 Jan 2021 13:00:17 No.12600289 Report

Quoted By:

>>12600156
Then you must lurk longer, the rabbit hole goes much deeper :/

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