Abstract
Many of the properties of a Weyl algebra An over a base field of non-zero characteristic are explained in terms of connections and curvatures on a vector bundle on an affine space X = A2n. In particular, it is known that an algebra endomorphism φ of An gives rise to a symplectic endomorphism f of X with a gauge transformation g. In this paper we study the converse problem of finding φ from an arbitrary symplectic endomorphism f of X = A2n. It is shown that, given such f , we may construct a projective left An-module (which corresponds to ‘the sheaf of local gauge transformations' ) such that its triviality is equivalent to the existence of the ‘lift' φ. Some properties of such a module will be discussed using the theory of reflexive sheaves.
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