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Extensions by C*‐Algebras of Real Rank Zero, III
Author(s) -
Lin H
Publication year - 1998
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611598000355
Subject(s) - mathematics , mathematics subject classification , unitary state , separable space , pure mathematics , zero (linguistics) , trace (psycholinguistics) , extension (predicate logic) , equivalence (formal languages) , rank (graph theory) , scalar (mathematics) , algebra over a field , discrete mathematics , combinatorics , mathematical analysis , linguistics , philosophy , geometry , political science , computer science , law , programming language
We give a complete classification (up to unitary equivalence) of extensions of C ( X ) by a separable simple AF‐algebra A with a unique trace (up to scalar multiples), where X is a compact subset of the plane. In particular, we show that there are non‐trivial extensions τ such that τ = 0 in Ext( C ( X ), A ). A new index is introduced to determine when an extension is trivial. Extensions of C ( S 2 ) and other algebras are also studied. Our results work for a larger class of C*‐algebras of real rank zero. 1991 Mathematics Subject Classification : primary 46L05, 46L35; secondary 46L80.