On cohomology of Lie algebras

Abstract

for all o1, * ,an in L. This definition makes Cn(L, M) into a G-module and further ,y (8f)=6(y yf) where a is the coboundary operator: Cn(L, M) -*Cn+'(L, M) so that the cohomology groups Hn(L, M) take on the structure of a G-module. Professor Hochschild suggested to the author that he define an operation of G on the standard interpretations of the low dimensional cohomology groups which would agree with the operation of G on Hn(L, M) as given above. This problem has an analogue in the cohomology of groups. There, if L is a normal subgroup of a group G and f is any function of Ln+' to M, the operation