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EnglishWe 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.
| Titolo: | Extending addition in Elliott's local semigroup | |
| Autori: | ||
| Data di pubblicazione: | 1993 | |
| Rivista: | ||
| 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. | |
| Handle: | http://hdl.handle.net/11390/674092 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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