Lie Algebra Extensions of the Poincaré Algebra

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Abstract
The ``linear'' counterpart of the problem of analytic group extensions of the Poincaré group is presented in terms of the considerably simpler (but less general) analysis of Lie algebra extensions of the Poincaré algebra P. After easily proving with this technique that every C kernel (P, θ) has an extension and that every such extension is inessential, the problem of analyzing the central extensions of P is carried out with the well‐expected result that every such extension is trivial. But contrary to some claims, we exhibit an example which explicitly shows an essential noncentral extension of P.

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