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Inductive limits, unique traces and tracial rank zero
Author(s) -
Brown Nathanial P.
Publication year - 2007
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/bdm007
Subject(s) - mathematics , rank (graph theory) , zero (linguistics) , trace (psycholinguistics) , pure mathematics , sense (electronics) , combinatorics , philosophy , chemistry , linguistics
In the program to classify C*‐algebras, it is very important to find abstract conditions which are sufficient to imply that a given algebra has tracial rank zero, in the sense of Huaxin Lin. Even in the presence of a unique trace, we show that the union of the known necessary conditions is not enough.