OAI/Analysis/PureInfiniteness/AbsorptionFromCentralCopy.lean
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Absorption from a central embedding and a connected approximate half-flip, using the nuclearity and simplicity of O∞ and Kirchberg's criterion.
- theorem
OAI.WeakPureInfiniteness.Campaign.nuclear_absorption_from_central_embedding_and_halfFlipline 25Source documentation
The full absorption corollary, still conditional on the published central embedding and connected half-flip; O∞ nuclearity and simplicity are proved.
theorem nuclear_absorption_from_central_embedding_and_halfFlip (U : Ultrafilter ℕ) [Fact ((U : Filter ℕ) ≤ atTop)] (hcentral : Nontrivial A → Nuclear A → StronglyPurelyInfinite A → Nonempty (OInfinity →⋆ₐ[ℂ] NonunitalGamma.CentralSequenceAlgebra (A := A) U)) …Mentions: OAI.WeakPureInfiniteness.Nuclear, OAI.WeakPureInfiniteness.StronglyPurelyInfinite, OAI.WeakPureInfiniteness.OInfinity, OAI.NonunitalGamma.CentralSequenceAlgebra