Representation of a compact Lie group

Adjoint representation

Given a Lie group 𝐺 with its corresponding Lie algebra 𝔤, we may define an adjoint representation Ad− :𝐺 →GL(𝔤) by conjugation lie

Ad𝑔:𝔤→𝔤𝑋↦𝑔𝑋𝑔−1

Induced Lie algebra representation

See Adjoint Lie algebra representation.

Properties

• Ad𝑒𝑋 =𝑒ad𝑋

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