1978
DOI: 10.2307/1971124
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A C ∗ -algebra  for which Ext() is not a Group

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Cited by 28 publications
(55 citation statements)
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“…We use the result to show that the Ext-invariant for the reduced C * -algebra of the free group on 2 generators is not a group but only a semi-group. This problem has been open since Anderson in 1978 found the first example of a C * -algebra A for which Ext(A) is not a group.…”
mentioning
confidence: 99%
“…We use the result to show that the Ext-invariant for the reduced C * -algebra of the free group on 2 generators is not a group but only a semi-group. This problem has been open since Anderson in 1978 found the first example of a C * -algebra A for which Ext(A) is not a group.…”
mentioning
confidence: 99%
“…(See Arveson [3] where all of this is put together nicely.) When A is not nuclear, Anderson [1] showed that Ext(A) is generally not a group. Recently Haagerup and Thorbjornsen [24] have shown that Ext of the reduced C*-algebra of the free group F 2 is not a group.…”
Section: Essentially Normal Operatorsmentioning
confidence: 99%
“…(1), suppose that there exists a C * -algebra D and an element x ∈ A D such that x E > x λ . Then the extension is not semi-invertible.…”
Section: Be Asymptotic Homomorphisms Then Their Tensor Product φ T ⊗mentioning
confidence: 99%
“…Beyond the nuclear case not much is known about the general classification of C * -extensions, but more and more examples of non-invertible extensions are coming up [1], [6], [13], [12], [5]. In [9], [10] we suggested weakening the notion of triviality for extensions so that more extensions would become invertible in this new sense.…”
mentioning
confidence: 99%