Lie algebra representation

In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator. In the language of physics, one looks for a vector space V {\displaystyle V} together with a collection of operators on V {\displaystyle V} satisfying some fixed set of commutation relations, such as the relations satisfied by the angular momentum operators.

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