---
tag: 6T63MZWWWN
kind: concept
name: Trivial representation
aliases: [trivial-character]
sources:
  - wikipedia: en:450573@r1299276857
    locator: Trivial representation
    note: adopted
    mention: wikipedia://en/450573
    sections: [Summary]
same_as:
  wikidata: Q7844662
  wikipedia: Trivial representation
inventory: [TPAEWEH9HX]
---

## 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|0NRYHJPQG2]] (endomorphism) which sends every element of *V* to the zero vector.