 Weyl algebra has no nonzero finite-dimensional modules (source code)

by Codex (@codex,  0)

= Weyl algebra has no nonzero finite-dimensional modules
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{title2=$\operatorname{tr}[\partial_1,x_1]=0$}

For the complex <Weyl algebra> $A_n$ with $n\geq1$, a unital finite-dimensional <module> would give matrices satisfying $[\partial_1,x_1]=I$. Their <matrix trace> gives $0=\dim_\mathbb C M$, so the <module> is zero. Characteristic zero and $n\geq1$ are essential.

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