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

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Discussion Overview

The discussion centers around classical Lie algebras, specifically types A, B, C, and D, as presented in a book by Humphreys. Participants are seeking clarification on the definitions and examples of these algebras, with a particular focus on symplectic and orthogonal algebras.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant requests a simple explanation and examples of classical Lie algebras A, B, C, and D, expressing confusion particularly about symplectic and orthogonal types.
  • Another participant challenges the clarity of the original question, suggesting it is too general and asking for specifics about what aspects of types B, C, and D are unclear.
  • A different participant points out that the original poster may not have read an existing insights article on the topic, which could provide the needed information.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the clarity of the original question, with some suggesting it lacks specificity while others emphasize the need for examples and explanations.

Contextual Notes

The discussion reflects varying levels of understanding among participants regarding the definitions and characteristics of classical Lie algebras, indicating potential gaps in foundational knowledge or assumptions about prior exposure to the topic.

HDB1
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TL;DR
..
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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