• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Algebra Chevalley Eilenberg Complex

  • Thread starter fresh_42
  • Start date

fresh_42

Mentor
Insights Author
2018 Award
10,296
7,015
Does anybody know a good book about especially the Chevalley Eilenberg complexes of arbitrary Lie algebras, i.e. not automatically semisimple Lie algebras, and where the Whitehead Lemmata are more an example than the main subject.

@lavinia, @A. Neumaier perhaps?
 

dextercioby

Science Advisor
Homework Helper
Insights Author
12,925
501
If you cannot find here: Azcarraga, J., Izquierdo, J. - Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics (CUP, 1995), then I wonder which better source you can get.
 

fresh_42

Mentor
Insights Author
2018 Award
10,296
7,015
If you cannot find here: Azcarraga, J., Izquierdo, J. - Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics (CUP, 1995), then I wonder which better source you can get.
Thanks, but they basically deal with Lie groups. The chapter about Lie algebras contains only the standard results as far as I can judge from the list of contents, and which are closely related to semisimple Lie algebras, as they are - with a few exceptions (Heisenberg, Poincaré) - the only ones with physical relevance. Then they have a little bit of the BRST calculus which again is physics.

I have some good books (Hilton - Stammbach, Varadarajan, Humphreys) and even one about group cohomology (Brown), but I'm especially interested in the Chevalley - Eilenberg - complex, will say where this approach leads to beside some basic classical results as the Whitehead lemmata. I have such a complex for non semisimple Lie algebras and try to figure out, whether there are substantial results or whether this approach is more or less hot air. One of my difficulties is, that although my Lie algebra is a linear one, I do not know a corresponding group; except some specific integrations in small dimensions of course.
 

Want to reply to this thread?

"Chevalley Eilenberg Complex" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top