# 2-cocycle for trivial Lie ring action

From Groupprops

## Definition

Suppose is a Lie ring and is an abelian group.

### Explicit definition

A **2-cocycle for trivial Lie ring action** is a homomorphism of groups (where is the external direct product of with itself) satisfying the following additional condition:

### Definition in terms of 2-cocycle

A **2-coycle for trivial Lie ring action** is a special case of a 2-cocycle for a Lie ring action in the case where the action is trivial.