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ACTIVE LATTICES DETERMINE AW*-ALGEBRAS

By Chris Heunen, Manuel and L. Reyes

Abstract

Abstract. We prove that AW*-algebras are determined by their projections, their symmetries, and the action of the latter on the former. 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. 1

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.7196
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