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Book Review
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Book Information
Author(s):
D. Evans and Y. Kawahigashi
Title:
Quantum symmetries on operator algebras
Additional book information:
Oxford Univ. Press,
New York,
1998,
xv + 829,
$200.00,
0-19-851175-2
References:
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-algebras. Transactions AMS 171, (1972), 195-234. MR 47:844 - [2]
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- S. Doplicher, R. Haag, J. Roberts, Local observables and particle statistics, I. Comm. Math. Phys. 23, (1971), 199-230. MR 45:6316
- [6]
- E. Effros, D. Handelman and C. Shen, Dimension groups and their affine representations. Amer. J. Math 102, (1980), 385-407. MR 83g:46061
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- J. Glimm, A. Jaffe, Quantum physics. A functional integral point of view. Springer-Verlag, New York-Berlin, 1981. MR 83c:81001
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- F.M. Goodman, P. de la Harpe, and V.F.R. Jones, Coxeter graphs and towers of algebras, Springer-Verlag, 1989. MR 91c:46082
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- R. Haag, Local quantum physics, Springer, Berlin, 1992. MR 94d:81001
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- U. Haagerup, Principal graphs of subfactors in the index range
in: ``Subfactors", World Scientific, Singapore-New Jersey-London-Hong Kong (1994) 1-39. MR 96d:46081 - [13]
- -, Connes' bicentraliser problem and uniqueness of the injective factor of type III
. Acta Math. 158, (1987), 95-148. MR 88f:46117 - [14]
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factors. Ann. of Math. 90, (1970), 372-377. MR 41:4261 - [17]
- F.J. Murray and J. von Neumann, On rings of operators. IV. Ann. of Math. 44, (1943), 716-808. MR 5:101a
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- M. Nakamura, Z. Takeda, A Galois theory for finite factors. Proc. Japan Acad. 36, (1960), 258-260. MR 23:A1246
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- A. Ocneanu, Actions of discrete amenable groups on von Neumann algebras. Springer Lecture Notes in Mathematics, 1138, (1985). MR 87e:46091
- [20]
- A. Ocneanu, Quantized group, string algebras and Galois theory for algebras in Operator algebras and applications, vol. 2, L.M.S lecture note series, 136, (1988), 119-172. MR 91k:46068
- [21]
- S. Popa, An axiomatization of the lattice of higher relative commutants of a subfactor, Invent. Math 120, (1995), 427-445. MR 96g:46051
- [22]
- S. Sawin, Subfactors constructed from quantum groups. Amer. J. Math. 117, (1995), no. 6, 1349-1369. MR 96h:46097
- [23]
- J. von Neumann, On rings of operators. Reduction theory, Ann. of Math. 50, (1949), 401-485. MR 10:548a
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- -, On rings of operators, III, Ann. of Math. 41, (1940), 94-161.
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- -, Zur Algebra der Funktionaloperationen und Theorie der normalen Operatoren, Math. Ann. 102, (1929), 370-427.
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- -, On infinite direct products, Compositio Math 6, (1938), 1-77.
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- A. Wassermann, Operator algebras and conformal field theory. III. Fusion of positive energy representations of
using bounded operators. Invent. Math. 133, (1998), 467-538. MR 99j:81101 - [28]
- H. Wenzl,
tensor categories from quantum groups. J. Amer. Math. Soc. 11, (1998), no. 2, 261-282. MR 98k:46123 - [29]
- F. Xu, Standard
-lattices from quantum groups. Invent. Math. 134, (1998), 455-487. MR 2000c:46123
Additional Information:
Reviewer(s):
Vaughan
F. R.
Jones
Affiliation:
University of California, Berkeley
Email:
vfr@math.berkeley.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
38
(2001),
369-377.
MSC
(2000):
Primary 46Lxx, 81T75, 81T45, 81T05, 81T40, 81T08, 57R56
DOI:
10.1090/S0273-0979-01-00906-5
PII:
S 0273-0979(01)00906-5
Posted:
March 27, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
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