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Notes on A 풯‐algebras and extensions of A 핋‐algebras by 풦
Author(s) -
Yao Hongliang,
Fang Xiaochun
Publication year - 2010
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdp124
Subject(s) - mathematics , cellular algebra , algebra over a field , division algebra , rank (graph theory) , filtered algebra , subalgebra , algebra representation , extension (predicate logic) , universal enveloping algebra , jordan algebra , zero (linguistics) , symmetric algebra , pure mathematics , invariant (physics) , combinatorics , computer science , linguistics , philosophy , programming language , mathematical physics
H. Lin and H. Su classified A ‐algebras of real rank zero. An A ‐algebra often becomes an extension of an A ‐algebra by an AF ‐algebra. In this paper, we define a new invariant pi( A ) of C*‐algebra A by partial isometries and give a necessary condition on which a C*‐algebra is an A ‐algebra. We demonstrate that there is an essential extension of an A ‐algebra with real rank zero by which is not an A ‐algebra.