| Title:
|
Unital extensions of $AF$-algebras by purely infinite simple algebras (English) |
| Author:
|
Liu, Junping |
| Author:
|
Wei, Changguo |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
989-1001 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we consider the classification of unital extensions of $AF$-algebras by their six-term exact sequences in $K$-theory. Using the classification theory of $C^*$-algebras and the universal coefficient theorem for unital extensions, we give a complete characterization of isomorphisms between unital extensions of $AF$-algebras by stable Cuntz algebras. Moreover, we also prove a classification theorem for certain unital extensions of $AF$-algebras by stable purely infinite simple $C^*$-algebras with nontrivial $K_1$-groups up to isomorphism. (English) |
| Keyword:
|
$AF$-algebra |
| Keyword:
|
extension |
| Keyword:
|
purely infinite simple algebra |
| MSC:
|
46L05 |
| MSC:
|
46L35 |
| idZBL:
|
Zbl 06433709 |
| idMR:
|
MR3304793 |
| DOI:
|
10.1007/s10587-014-0148-z |
| . |
| Date available:
|
2015-02-09T17:34:26Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144156 |
| . |
| Reference:
|
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