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What is a reference for the subject of "free resolutions for Lie algebras"?

Does the term "standard resolutions" means "free resolutions"?

What is a "bar resolution"?

Is there only one way to talk about this or it is always by considering the Lie algebra as a module over its universal enveloping algebra?

These questions arose when I was reading some papers by K. S. Brown

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  • $\begingroup$ jim stasheff asked on this site a few days ago about free resolutions for Lie algebras. $\endgroup$
    – Mariano Suárez-Álvarez
    Commented May 19, 2013 at 2:39
  • $\begingroup$ Namely, mathoverflow.net/questions/130376/resolutions-of-lie-algebras $\endgroup$
    – Allen Knutson
    Commented May 19, 2013 at 3:10
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    $\begingroup$ I guess you all are suggesting a question which is not clear, since the person is talking about "DG-algebras" without definition and motivation. The answer which was gave there by Mariano Suárez seems to be something correctly, but not basic and without a reference! The other answer is talking about a paper which seems so far from the topic stated here. I will accept the answer given by Dietrich, because it is what make sense and helpful. $\endgroup$
    – Binai
    Commented May 19, 2013 at 18:00

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Here are some references (which are not mentioned in Resolutions of Lie algebras).

First I can recommend the book of Charles A. Weibel, An Introduction to Homological Algebra. It answers your questions and has a chapter where the general theory is made explicit for Lie algebras.

Secondly, the book of A. W. Knapp on Lie groups, Lie algebras and cohomology. This has many details and many examples.

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  • $\begingroup$ May I ask, in the resolution $V_\ast$ of $U(\mathfrak{g})$-module $k$, what does the letter $V$ stand for, i.e. who is this resolution named after? $\endgroup$
    – Leo
    Commented Mar 24, 2014 at 0:27

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