# Why Lie algebra (Chevalley–Eilenberg) cohomology are graded Lie algebras but not G-algebras?

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 G-algebras(Gerstenhaber algebra)". Can anyone please explain me the reason for the mentioned result?

• 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. – Nicola Ciccoli Jul 28 '18 at 5:33
• It would be nice if you refer me something to read... – Ripan Saha Jul 28 '18 at 5:44
• emis.de/journals/AM/09-4/roger.pdf – Nicola Ciccoli Jul 28 '18 at 7:51