I was reading a paper related to Gerstenhaber algebra structure and came across to this "Lie algebra (Chevalley–Eilenberg) cohomology are graded Lie algebras but not Galgebras(Gerstenhaber algebra)". Can anyone please explain me the reason for the mentioned result?
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2$\begingroup$ It is always difficult to say why somethong does NOT have a property. If you think of Lie cocycles as left invariant differential form this means you should have a naturally defined Lie bracket on l.i. $1$forms, which is not the case of a generic Lie group. $\endgroup$ – Nicola Ciccoli Jul 28 '18 at 5:33

$\begingroup$ It would be nice if you refer me something to read... $\endgroup$ – Ripan Saha Jul 28 '18 at 5:44

1$\begingroup$ emis.de/journals/AM/094/roger.pdf $\endgroup$ – Nicola Ciccoli Jul 28 '18 at 7:51