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

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Classical Lie algebras A, B, C, and D are defined in Humphreys' book, but the discussion highlights confusion around the symplectic and orthogonal types. The initial inquiry seeks simple examples to clarify these concepts. Respondents emphasize the need for more specific questions regarding the understanding of each type. A suggestion is made to refer to an existing article that provides insights into Lie algebras. The conversation underscores the complexity of these algebraic structures and the importance of targeted questions for effective learning.
HDB1
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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,
 
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HDB1 said:
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?
 
Dear @martinbn,

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

Thanks,
 
HDB1 said:
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?
 
HDB1 said:
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
 

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