Semisimplicity and global dimension of a finite von Neumann algebra
Mathematica Bohemica (2007)
- Volume: 132, Issue: 1, page 13-26
- ISSN: 0862-7959
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topVaš, Lia. "Semisimplicity and global dimension of a finite von Neumann algebra." Mathematica Bohemica 132.1 (2007): 13-26. <http://eudml.org/doc/250246>.
@article{Vaš2007,
abstract = {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.},
author = {Vaš, Lia},
journal = {Mathematica Bohemica},
keywords = {finite von Neumann algebra; algebra of affiliated operators; semisimple ring; global dimension; algebra of affiliated operators; semisimple ring; global dimension},
language = {eng},
number = {1},
pages = {13-26},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Semisimplicity and global dimension of a finite von Neumann algebra},
url = {http://eudml.org/doc/250246},
volume = {132},
year = {2007},
}
TY - JOUR
AU - Vaš, Lia
TI - Semisimplicity and global dimension of a finite von Neumann algebra
JO - Mathematica Bohemica
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 132
IS - 1
SP - 13
EP - 26
AB - 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.
LA - eng
KW - finite von Neumann algebra; algebra of affiliated operators; semisimple ring; global dimension; algebra of affiliated operators; semisimple ring; global dimension
UR - http://eudml.org/doc/250246
ER -
References
top- 10.1002/mana.19931640118, Math. Nachr. 164 (1993), 259–270. (1993) MR1251467DOI10.1002/mana.19931640118
- 10.1216/RMJ-1982-12-1-149, Rocky Mt. J. Math. 12 (1982), 149–164. (1982) Zbl0484.46054MR0649748DOI10.1216/RMJ-1982-12-1-149
- Baer -rings, Die Grundlehren der mathematischen Wissenschaften, 195, Springer, 1972. (1972) MR0429975
- Von Neumann Algebras, North Holland, Amsterdam, 1981. (1981) Zbl0473.46040MR0641217
- Algebra, Reprint of the 1974 original, Graduate Texts in Mathematics, 73, Springer, Berlin, 1980. (1980) Zbl0442.00002MR0600654
- Les foncteurs dérivés de et leurs applications en théorie des modules, Lecture Notes in Mathematics, 254, Springer, Berlin, 1972. (1972) MR0407091
- Fundamentals of the Theory of Operator Algebras, volume 1: Elementary Theory, Pure and Applied Mathematics Series, 100, Academic Press, London, 1983. (1983) MR0719020
- Fundamentals of the Theory of Operator Algebras, volume 2: Advanced Theory, Pure and Applied Mathematics Series, 100, Academic Press, London, 1986. (1986) MR0859186
- Lectures on Modules and Rings, Graduate Texts in Mathematics, 189, Springer, New York, 1999. (1999) Zbl0911.16001MR1653294
- -invariants: Theory and Applications to Geometry and K-theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Folge 3, 44, Springer, Berlin, 2002. (2002) Zbl1069.57017MR1926649
- Algebraic -theory and Its Applications, Graduate Texts in Mathematics, 147, Springer, New York, 1994. (1994) Zbl0801.19001MR1282290
- 10.1081/AGB-200049871, Commun. Alg. 33 (2005), 663–688. (2005) Zbl1108.46044MR2128403DOI10.1081/AGB-200049871
- 10.1016/j.jalgebra.2005.02.018, J. Alg. 289 (2005), 614–639. (2005) MR2142388DOI10.1016/j.jalgebra.2005.02.018
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