Open AccessOn Rørdam's classification of certain $C^*$-algebras with one non-trivial ideal, II
Author(s) -
Gunnar Restorff,
Efren Ruiz
Publication year - 2007
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-15045
Subject(s) - unital , mathematics , ideal (ethics) , class (philosophy) , unit (ring theory) , pure mathematics , discrete mathematics , algebra over a field , mathematics education , artificial intelligence , computer science , epistemology , philosophy
In this paper we extend the classification results obtained by Rørdam in the paper [16]. We prove a strong classification theorem for the unital essential extensions of Kirchberg algebras, a classification theorem for the non-stable, non-unital essential extensions of Kirchberg algebras, and we characterize the range in both cases. The invariants are cyclic six term exact sequences together with the class of some unit.