Abstract
Let A be a \({\mathbb{k}}\)-algebra and \({A[t; \alpha,\delta]}\) its Ore extension. We give a pair of adjoint functors between the module category over ker \(\delta\) and the module category over \({A[t; \alpha,\delta]}\). For a kind of special Ore extensions, this pair describes an equivalence between the module category over ker \({\delta}\) and an appropriate subcategory of the module category over \({A[t; \alpha,\delta]}\). Applied to the case of Weyl algebras, this is exactly a Kashiwara’s theorem about D-modules.
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