The Hochschild-Serre spectral sequence

In this section we fix a graded Lie algebra, L = L i i∈ℤ, with universal enveloping algebra UL. If M is a left (right) UL-module then restriction of the action of UL to L defines a left (right) representation of L in M, and this correspondence is a bijection ( §21 (a)). We use this to identify L-modules as UL-modules and conversely. In particular, the trivial representation of L in \(\Bbbk \) defines a canonical (left and right) UL-module structure in \(\Bbbk \).