High Quality Content by WIKIPEDIA articles! In mathematics, the adjoint endomorphism or adjoint action is an endomorphism of Lie algebras that plays a fundamental role in the development of the theory of Lie algebras and Lie groups. Given an element x of a Lie algebra , one defines the adjoint action of x on as the endomorphism with adx(y) = [x,y] for all y in . adx is an action that is linear. In mathematics, the adjoint endomorphism or adjoint action is an endomorphism of Lie algebras that plays a fundamental role in the development of the theory of Lie algebras and Lie groups. Given an element x of a Lie algebra , one defines the adjoint action of x on as the endomorphism with adx(y) = [x,y] for all y in . adx is an action that is linear.

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