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Extensions of Inductive Limits of Circle Algebras
Author(s) -
Lin Huaxin,
Rørdam Mikael
Publication year - 1995
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/51.3.603
Subject(s) - zero (linguistics) , rank (graph theory) , direct limit , mathematics , limit (mathematics) , extension (predicate logic) , pure mathematics , real number , discrete mathematics , combinatorics , algebra over a field , mathematical analysis , computer science , philosophy , linguistics , programming language
A classic result of L. G. Brown [ 3 ] and G. Elliott [ 7 ] says that every extension of two AF‐algebras is again an AF‐algebra. We generalize this result to the larger class of C∗‐algebras which are inductive limits of circle algebras and have real rank zero. Let E be an extension of C∗‐algebras A and B ,0 → A → E → B → 0 ,where A and B have real rank zero and are inductive limits of circle algebras. If E has real rank zero and stable rank one, then it is an inductive limit of circle algebras. Moreover, E has real rank zero and is an inductive limit of circle algebras if and only if the extension satisfies the condition that the index maps K j ( B ) → K 1− j ( A ) for j = 0,1, are zero.