Stable flatness of nonarchimedean hyperenveloping algebras

Mathematics – Representation Theory

Scientific paper

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Scientific paper

Let L be a p-adic local field and g a finite dimensional Lie algebra over L.
We show that its hyperenveloping algebra F(g) is a stably flat completion of
its universal enveloping algebra. As a consequence the relative cohomology for
the locally convex algebra F(g) coincides with the underlying Lie algebra
cohomology.

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