Abstract
In this paper we show that neither the Weyl algebra $A_n(K)$ nor the derivative algebra $DA_n(K)$ has infinite irreducible representations in the case when the ground field $K$ has characteristic $p \gt 0$. We also give a complete classification of irreducible representations of the first derivative algebra $DA_1$ when $K$ is algebraically closed. Finally, we present an algorithm that determines, in finitely many steps, whether $DA_1/L$ is a simple $DA_1$-module, where $L$ is any left ideal of $DA_1$.
Citation
Jiangfeng Zhang. Jianghua Zhang. "On the representation of derivative algebras in characteristic $p \gt 0$." Illinois J. Math. 46 (1) 45 - 61, Spring 2002. https://doi.org/10.1215/ijm/1258136139
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