Lie algebra representation homomorphism
= Lie algebra representation homomorphism
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{title2=$T(xv)=xT(v)$}
A linear map between <Lie algebra representations> is a representation homomorphism when it commutes with the action of every element. Its <kernel> and <image of a linear map> are invariant subspaces. This is a map of modules, distinct from a <Lie algebra homomorphism> between the acting algebras themselves.