Abstract
When Clifford algebras are studied in relation with exterior algebras, it is easy to undertake a parallel study of “symplectic Clifford algebras”, also called “Weyl algebras”: it suffices to replace exterior algebras with symmetric algebras, to remove all “twisting signs” from all places where they are present, and to intrude them into all places where they are absent. This enables one to imagine a symplectic counterpart of a theorem of Lipschitz about orthogonal transformations; unfortunately this counterpart needs an “enlargement” of the Weyl algebra, and leads to infinite sums and convergence problems. Some specific problems of the symplectic case, that result from this enlargement and that cannot be treated by purely algebraic means, are commented upon.
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