Adjoint representation

Given a Lie group $𝐺$ with its corresponding Lie algebra $𝔤$ , we may define an adjoint representation $A d - : 𝐺 \to G L (𝔤)$ by conjugation #m/def/lie

A d 𝑔 : 𝔤 \to 𝔤 𝑋 \mapsto 𝑔 𝑋 𝑔 - 1

Induced Lie algebra representation

See Adjoint Lie algebra representation.

Properties

$A d 𝑒 𝑋 = 𝑒 a d 𝑋$

#state/stub | #lang/en | #SemBr