We study the unique extendability of Elliott′s partial addition of Murray-von Neumann equivalence classes of projections in AF C*-algebras. We prove that there is at most one commutative associative monotone extension satisfying the natural residuation condition that for each projection p the class of 1 - p is the smallest one whose sum with the class of p equals 1. We prove that for every AF C*-algebra A this associative commutative monotone residual extension exists if, and only if, the Murray-von Neumann order on equivalence classes of projections in A is a lattice order. By Elliott′s classification theorem, the resulting monoid uniquely characterizes A. We give a simple equational characterization of the monoids arising as classifiers.

EXTENDING ADDITION IN ELLIOTT'S LOCAL SEMIGROUP / D. MUNDICI; G. PANTI. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 117:(1993), pp. 461-471. [10.1006/jfan.1993.1134]

EXTENDING ADDITION IN ELLIOTT'S LOCAL SEMIGROUP

MUNDICI, DANIELE;
1993

Abstract

We study the unique extendability of Elliott′s partial addition of Murray-von Neumann equivalence classes of projections in AF C*-algebras. We prove that there is at most one commutative associative monotone extension satisfying the natural residuation condition that for each projection p the class of 1 - p is the smallest one whose sum with the class of p equals 1. We prove that for every AF C*-algebra A this associative commutative monotone residual extension exists if, and only if, the Murray-von Neumann order on equivalence classes of projections in A is a lattice order. By Elliott′s classification theorem, the resulting monoid uniquely characterizes A. We give a simple equational characterization of the monoids arising as classifiers.
1993
117
461
471
D. MUNDICI; G. PANTI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/312110
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