Representation of Lie Algebras

Representation of Lie Algebras

Let $\mathfrak{g}$ be a Lie algebra over a field $F$. A representation of $\text{g}$ on a vector space $V$ is a Lie algebra homomorphism $\rho :\text{g}\to \mathfrak{gl}(V)$ where $\text{gl}(V)$ is the Lie algebra of all linear endomorphisms on $V$.