Cocycle for a group action
Definition in terms of bar resolution
A -cocycle is an element in the cocycle group for the Hom complex from the bar resolution of to , in the sense of -modules.
For a nonnegative integer, a -cocycle for the action of on is a function such that, for all :
If we suppress the symbol and denote the action by , this becomes:
In particular, when the action is trivial, this is equivalent to saying that: