| Title:
|
Semisimplicity and global dimension of a finite von Neumann algebra (English) |
| Author:
|
Vaš, Lia |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
132 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
13-26 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that a finite von Neumann algebra ${\mathcal{A}}$ is semisimple if the algebra of affiliated operators ${\mathcal{U}}$ of ${\mathcal{A}}$ is semisimple. When ${\mathcal{A}}$ is not semisimple, we give the upper and lower bounds for the global dimensions of ${\mathcal{A}}$ and ${\mathcal{U}}.$ This last result requires the use of the Continuum Hypothesis. (English) |
| Keyword:
|
finite von Neumann algebra |
| Keyword:
|
algebra of affiliated operators |
| Keyword:
|
semisimple ring |
| Keyword:
|
global dimension |
| MSC:
|
16E10 |
| MSC:
|
16K99 |
| MSC:
|
16W99 |
| MSC:
|
46L10 |
| MSC:
|
46L99 |
| idZBL:
|
Zbl 1171.46317 |
| idMR:
|
MR2311749 |
| DOI:
|
10.21136/MB.2007.133990 |
| . |
| Date available:
|
2009-09-24T22:28:31Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133990 |
| . |
| Reference:
|
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| Reference:
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| . |
