What is the (co)homology of a free (graded) Lie algebra?

Asked Jan 18 '21 at 17:45

Active Jan 20 '21 at 19:53

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In characteristic $0$, what is the Chevalley-Eilenberg (co)homology of a free (graded) Lie algebra? Not the definition, but $H^i =$ ??

edited Jan 20 '21 at 19:53

Ottavio

asked Jan 18 '21 at 17:45

Jim Stasheff

1

Which coefficients? Cartan and Eilenberg’s antisymmetrisation map $F^∗$ provides an explicit identification between the Chevalley-Eilenberg cohomology of a free Lie algebra $L$ and the Hochschild cohomology of its universal enveloping algebra $U(L)$. – Dietrich Burde Jan 18 '21 at 17:53
In Weibel's book An Intro to Homological Algebra, he H^(L;M)=0 for \geq 2 for L free Lie, but there is no mention of the graded case.Is it known? – Jim Stasheff Jan 24 '21 at 20:55

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