# Definition The trivial [[Group Representation|representation]] of a [[group]] $G$ on a [[vector space]] $V$ is given by: $ \Pi(g) = I \quad \forall g \in G $ The trivial representation of [[Lie algebra|Lie algebras]] is [[Induced Lie Algebra Homomorphism|given by]]: $ \pi(X) = \frac{d}{dt} \Pi(e^{tX}) = 0 \quad \forall X \in \mathfrak{g} $