Trivial representation

Summary

In the mathematical field of representation theory, a trivial representation is a representation $(V,\,\varphi)$ of a group G on which all elements of G act as the identity mapping of V. A trivial representation of an associative or Lie algebra is an (Lie) algebra representation for which all elements of the algebra act as the zero linear map (endomorphism) which sends every element of V to the zero vector.