Extensions by C*‐Algebras of Real Rank Zero, III | Zendy

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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.

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