Active lattices determine AW*-algebras

Chris Heunen, Manuel L. Reyes

Research output: Contribution to journalArticlepeer-review


We prove that operator algebras that have enough projections are completely determined by those projections, their symmetries, and the action of the latter on the former. This includes all von Neumann algebras and all AW*-algebras. We introduce active lattices, which are formed from these three ingredients. More generally, we prove that the category of AW*-algebras is equivalent to a full subcategory of active lattices. Crucial ingredients are an equivalence between the category of piecewise AW*-algebras and that of piecewise complete Boolean algebras, and a refinement of the piecewise algebra structure of an AW*-algebra that enables recovering its total structure.
Original languageEnglish
Pages (from-to)289-313
Number of pages25
JournalJournal of mathematical analysis and applications
Issue number1
Early online date26 Feb 2014
Publication statusPublished - 1 Aug 2014


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