Adjoint Representation of gl

[onyx pebble]

Let $G:=GL(n,\mathbb{F})$, $\mathfrak{g}:=gl(n,\mathbb{F})$, and let $U:=\mathbb{C}^n$ be the standard reprsentation. Prove the adjoint representation of $G$ and $\mathfrak{g}$ are isomorphic to $U\otimes U^\ast$.

[dark elbow]

Omegabet_

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[onyx pebble]

Mostly confused on how to go about the Lie algebra side of the question.

[slow frost]

Not gonna lie, idk what that is

[fair narwhal]

Lie algebras has been something I've been meaning to study for quite some time. Are you pulling these exercises from a particular book?

[onyx pebble]

no, from my course homework

[fair narwhal]

Ahhh. Are you/the course using a book or other source you would recommend?