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Book Information

Author(s): Ola Bratteli
Title: Derivations, dissipations and group actions on $C^ *$-algebras
Additional book information: Lecture Notes in Mathematics, vol. 1229, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1986, vi + 277 pp., $23.60. ISBN 0-387-17199-1

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2.: B. Blackadar, K-theory for operator algebras, Springer-Verlag, New York, 1986. MR 2188261
3.: O. Bratteli, G. A. Elliott and P. E. T. Jorgensen, Decomposition of unbounded derivations into invariant and approximately inner parts, J. Reine Angew. Math. 346 (1984), 166-193. MR 727402
4.: O. Bratteli, G. A. Elliott, F. M. Goodman and P. E. T. Jorgensen, Smooth Lie group actions on non-commutative tori, Preprint, 1986.; 5a. O. Bratteli and D. W. Robinson, Unbounded derivations of C*-algebras, Comm. Math. Phys. 42 (1975), 253-268. MR 377526; 5b. O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics. I, II, Springer-Verlag, New York, 1979/81 (vol. I in new ed., 1987).; 6a. A. Connes, C*-algèbres et géométrie différentielle, C. R. Acad. Sci. Paris 290 (1980), 599-604. MR 572645; 6b. A. Connes, Noncommutative differential geometry. I, The Chern character in K-homology; II, deRham homology and noncommutative algebra, Publ. Math. IHES 62 (1985). MR 823176
7.: J. Dixmier, Les algèbres d'opérateurs dans l'espace Hilbertien, 2nd ed., Gauthier-Villars, Paris, 1969.
8.: G. A. Elliott, Some C*-algebras with outer derivations. III, Ann. of Math. (2) 106 (1977), 121-143. MR 448093
9.: R. Haag, N. M. Hugenholtz and M. Winnink, On the equilibrium states in quantum statistical mechanics, Comm. Math. Phys. 5 (1967), 215-236. MR 219283; 10a. P. E. T. Jorgensen and R. T. Moore, Operator commutation relations, D. Reidel Publishing Co., Dordrecht-Boston, 1984. MR 746138; 10b. P. E. T. Jorgensen and P. S. Muhly (eds. ), Operator algebras and mathematical physics, Contemp. Math., vol. 62, Amer. Math. Soc., Providence, R. I., 1987. MR 878371; 11a. R. V. Kadison, Transformation of states in operator theory and dynamics, Topology 3 (1965), 177-198. MR 169073; 11b. R. V. Kadison (ed. ), Operator algebras and applications, Proc. Sympos. Pure Math., vol. 38, parts 1 and 2, Amer. Math. Soc., Providence, R. I., 1982. MR 679692; 12a. R. V. Kadison and J. R. Ringrose, Cohomology of operator algebras. I, Type I von Neumann algebras, Acta Math. 126 (1971), 224-244. MR 283578; 12b. R. V. Kadison and J. R. Ringrose, Fundamentals of the theory of operator algebras, vols. I and II, Academic Press, 1983/86. MR 719020
13.: I. Kaplansky, Modules over operator algebras, Amer. J. Math. 75 (1953), 839-859. MR 58137
14.: T. Kato, Perturbation theory for linear operators, Springer-Verlag, New York, 1976. MR 407617
15.: D. Montgomery and L. Zippin, Topological transformation groups, Interscience Publishers, Inc., New York, 1955. MR 73104
16.: R. T. Powers, Resistance inequalities for KMS-states of the isotropic Heisenberg model, Comm. Math. Phys. 51 (1976), 151-156. MR 426743
17.: R. T. Powers and S. Sakai, Existence of ground states and KMS states for approximately inner dynamics, Comm. Math. Phys. 39 (1975), 273-288. MR 359623
18.: M. A. Rieffel, C*-algebras associated with irrational rotations, Pacific J. Math. 93 (1981), 415-429. MR 623572; 19a. S. Sakai, On a conjecture of Kaplansky, Tôhoku Math. J. 12 (1960), 31-33. MR 112055; 19b. S. Sakai, The theory of unbounded derivatives in C*-algebras, Lecture Notes, Univ. of Newcastle, England, 1977.
20.: I. E. Segal, Notes towards the construction of nonlinear relativistic quantum fields. III, Properties of the C*-dynamics for a certain class of interactions, Bull. Amer. Math. Soc. 75 (1969), 1390-1395. MR 251992
21.: Ja. G. Sinaĭ and A. Ja. Helmskiĭ, A description of differentiations in algebras of the type of local observables of spin systems, Funktsional Anal. i Prilozhen 6 (1972), 99-100; English transl., Funct. Anal. Appl. 6 (1973), 343-344. MR 317686
22.: H. Takai, On a problem of Sakai in unbounded derivations, J. Funct. Anal. 43 (1981), 202-208. MR 633976
23.: C. -T. Yang, Hilbert's fifth problem and related problems on transformation groups, Proc. Sympos. Pure Math., vol. 28, Amer. Math. Soc., Providence, R. I., 1976, pp. 142-146. MR 425999

Review Information:
Journal: Bull. Amer. Math. Soc. 17 (1987), 202-209.
DOI: 10.1090/S0273-0979-1987-15565-0
PII: S 0273-0979(1987)15565-0

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