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Stably flat completions of universal enveloping algebras

Let 𝔤 be a complex Lie algebra, and let U(𝔤) be its universal enveloping algebra. We study homological properties of topological Hopf algebras containing U(𝔤) as a dense subalgebra. Specifically, let θ: U(𝔤) → H be a homomorphism to a topological Hopf algebra H. Assuming that H is either a nuclear Fréchet space or a nuclear (DF)-space, we formulate conditions on the dual algebra, H', that are sufficient for H to be stably flat over U(𝔤) in the sense of A. Neeman and A. Ranicki (2001) (i.e.,...

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