I What Are Classical Lie Algebras A, B, C, and D?

[HDB1]

TL;DR

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Dear @fresh_42 , Hope you are well.

Please, I have a question if you do not mind, about Lie Algebra,

In page 2 in the book of Lie algebra, written by Humphreys,

Classical Lie algebras, $A, B, C$ and $D$, I did not get it well, especially, symplectic and orthogonal..

Could you please explain with simple example of them.

Sorry for bothering you, and thank you so much in advance,

 

[martinbn]

TL;DR Summary: ..

Dear @fresh_42 , Hope you are well.

Please, I have a question if you do not mind, about Lie Algebra,

In page 2 in the book of Lie algebra, written by Humphreys,

Classical Lie algebras, $A, B, C$ and $D$, I did not get it well, especially, symplectic and orthogonal..

Could you please explain with simple example of them.

Sorry for bothering you, and thank you so much in advance,

You are asking him to write a book chapter! You need to be more specific. Did you get type A? What exactly did you not understand about B, C and D?

 

[HDB1]

Dear @martinbn,

No, classical lie algebras A,B,C, and D are not chapters, they are definitions in page number 2.

Thanks,

 

[martinbn]

Dear @martinbn,

No, classical lie algebras A,B,C, and D are not chapters, they are definitions in page number 2.

Thanks,

I know what they are! My point is that your question is too general.

I can ask you again. Did you understand type A? What exactly do you find unclear about types B, C and D?

 

[jbergman]

TL;DR Summary: ..

Dear @fresh_42 , Hope you are well.

Please, I have a question if you do not mind, about Lie Algebra,

In page 2 in the book of Lie algebra, written by Humphreys,

Classical Lie algebras, $A, B, C$ and $D$, I did not get it well, especially, symplectic and orthogonal..

Could you please explain with simple example of them.

Sorry for bothering you, and thank you so much in advance,

He has already written an insights article about this. Have you read it? https://www.physicsforums.com/insig...h-the-basics/#3-Classical-simple-Lie-Algebras