Liftings of diagrams of semilattices by diagrams of dimension groups

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dc.creatorTuma, Jiri
dc.creatorWehrung, Friedrich
dc.date2005-01-22
dc.date.accessioned2026-07-07T05:16:17Z
dc.date.available2026-07-07T05:16:17Z
dc.descriptionWe investigate categorical and amalgamation properties of the functor Idc assigning to every partially ordered abelian group G its semilattice of compact ideals Idc G. Our main result is the following. Theorem 1. Every diagram of finite Boolean semilattices indexed by a finite dismantlable partially ordered set can be lifted, with respect to the Idc functor, by a diagram of pseudo-simplicial vector spaces. Pseudo-simplicial vector spaces are a special kind of finite-dimensional partially ordered vector spaces (over the rationals) with interpolation. The methods introduced make it also possible to prove the following ring-theoretical result. Theorem 2. For any countable distributive join-semilattices S and T and any field K, any (v,0)-homomorphism $f: S\to T$ can be lifted, with respect to the Idc functor on rings, by a homomorphism $f: A\to B$ of K-algebras, for countably dimensional locally matricial algebras A and B over K. We also state a lattice-theoretical analogue of Theorem 2 (with respect to the Conc functor, and we provide counterexamples to various related statements. In particular, we prove that the result of Theorem 1 cannot be achieved with simplicial vector spaces alone.
dc.identifierhttps://arxiv.org/abs/math/0501376
dc.identifierhttp://arxiv.org/abs/math/0501376
dc.identifierProceedings of the London Mathematical Society 87, no. 3 (2003) 1--28
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73930
dc.subjectGeneral Mathematics
dc.subjectK-Theory and Homology
dc.subjectRings and Algebras
dc.subject06A12, 06C20, 06F20, 15A03, 15A24, 15A48, 16E20, 16E50, 19A49, 19K14
dc.titleLiftings of diagrams of semilattices by diagrams of dimension groups
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