= Schur algebra
{c}
{title2=$S(m,n)=\operatorname{End}_{\mathbb CS_n}((\mathbb C^m)^{\otimes n})$}
{wiki}
The Schur algebra is the <commutant> of place permutations on a <tensor power>. It is the linear span of the diagonal <general linear group> action, by <Schur–Weyl duality>. <Modules> over $S(m,n)$ correspond to homogeneous degree-$n$ <polynomial representations>. Over the <complex numbers> it is a <semisimple algebra>: decompose the <tensor power> as a <module> for the semisimple <group algebra> $\mathbb CS_n$, and take its endomorphism algebra.
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