Bulletin of the American Mathematical Society

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Book Information:

Authors: Erik M. Alfsen and Frederic W. Shultz
Title: State spaces of operator algebras: Basic theory, orientations, and C*-products
Additional book information: Birkhäuser Boston, Boston, MA, 2001, xii + 350 pp., ISBN 0-8176-3890-3, $69.95$

Authors: Erik M. Alfsen and Frederic W. Shultz
Title: Geometry of state spaces of operator algebras
Additional book information: Birkhäuser Boston, Boston, MA, 2003, xiv + 467 pp., ISBN 0-8176-4319-2, $74.95$

Erik M. Alfsen and Frederic W. Shultz, State spaces of Jordan algebras, Acta Math. 140 (1978), no. 3-4, 155–190. MR 472949, DOI 10.1007/BF02392307

Erik M. Alfsen, Harald Hanche-Olsen, and Frederic W. Schultz, State spaces of $C^{\ast }$-algebras, Acta Math. 144 (1980), no. 3-4, 267–305. MR 573454, DOI 10.1007/BF02392126

John C. Baez, The octonions, Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 2, 145–205. MR 1886087, DOI 10.1090/S0273-0979-01-00934-X

Ola Bratteli and Derek W. Robinson, Operator algebras and quantum statistical mechanics. 2, 2nd ed., Texts and Monographs in Physics, Springer-Verlag, Berlin, 1997. Equilibrium states. Models in quantum statistical mechanics. MR 1441540, DOI 10.1007/978-3-662-03444-6

A. Connes, A survey of foliations and operator algebras, Operator algebras and applications, Part 1 (Kingston, Ont., 1980) Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc., Providence, R.I., 1982, pp. 521–628. MR 679730

Joachim Cuntz and Wolfgang Krieger, A class of $C^{\ast }$-algebras and topological Markov chains, Invent. Math. 56 (1980), no. 3, 251–268. MR 561974, DOI 10.1007/BF01390048

7.

J. Dixmier, Anneaux d'opérateurs et représentations des groupes, Séminaire Bourbaki, Vol. 1, Exp. No. 40, pp. 331-336, Soc. Math. France, Paris, 1995.

8.

G. G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Monographs and Texts in Physics and Astronomy, Wiley-Interscience, New York, 1972.

Bruno Iochum and Frederic W. Shultz, Normal state spaces of Jordan and von Neumann algebras, J. Functional Analysis 50 (1983), no. 3, 317–328. MR 695418, DOI 10.1016/0022-1236(83)90008-3

Vaughan F. R. Jones, Subfactors and knots, CBMS Regional Conference Series in Mathematics, vol. 80, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1991. MR 1134131, DOI 10.1090/cbms/080

C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13

G. G. Kasparov, Equivariant $KK$-theory and the Novikov conjecture, Invent. Math. 91 (1988), no. 1, 147–201. MR 918241, DOI 10.1007/BF01404917

G. G. Kasparov and G. Skandalis, Groups acting on buildings, operator $K$-theory, and Novikov’s conjecture, $K$-Theory 4 (1991), no. 4, 303–337. MR 1115824, DOI 10.1007/BF00533989

Wilhelm Kaup, Jordan algebras and holomorphy, Functional analysis, holomorphy, and approximation theory (Proc. Sem., Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1978) Lecture Notes in Math., vol. 843, Springer, Berlin, 1981, pp. 341–365. MR 610837

N. P. Landsman, Quantization as a functor, Quantization, Poisson brackets and beyond (Manchester, 2001) Contemp. Math., vol. 315, Amer. Math. Soc., Providence, RI, 2002, pp. 9–24. MR 1958827, DOI 10.1090/conm/315/05471

N. Christopher Phillips, Continuous-trace $C^*$-algebras not isomorphic to their opposite algebras, Internat. J. Math. 12 (2001), no. 3, 263–275. MR 1841515, DOI 10.1142/S0129167X01000642

Ángel Rodríguez-Palacios, Jordan structures in analysis, Jordan algebras (Oberwolfach, 1992) de Gruyter, Berlin, 1994, pp. 97–186. MR 1293318

Robert M. Wald, Quantum field theory in curved spacetime and black hole thermodynamics, Chicago Lectures in Physics, University of Chicago Press, Chicago, IL, 1994. MR 1302174

1.

E. M. Alfsen and F. W. Shultz, State spaces of Jordan algebras, Acta Math. 140 (1978), 155-190. MR 0472949

2.

E. M. Alfsen, H. Hanche-Olsen, and F. W. Shultz, State spaces of C*-algebras, Acta Math. 144 (1980), 267-305. MR 0573454

3.

J. Baez, The octonions, Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 2, 145-205. MR 1886087

4.

O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics 2: Equilibrium States, Models in Quantum Statistical Mechanics (Second edition), Texts and Monographs in Physics, Springer-Verlag, Berlin, 1997. MR 1441540

5.

A. Connes, A survey of foliations and operator algebras, Operator Algebras and Applications, Part I (Kingston, Ont., 1980), pp. 521-628, Proc. Sympos. Pure Math. 38, Amer. Math. Soc., Providence, RI, 1982. MR 0679730

6.

J. Cuntz and W. Krieger, A class of C*-algebras and topological Markov chains, Invent. Math. 56 (1980), no. 3, 251-268. MR 0561974

7.

J. Dixmier, Anneaux d'opérateurs et représentations des groupes, Séminaire Bourbaki, Vol. 1, Exp. No. 40, pp. 331-336, Soc. Math. France, Paris, 1995.

8.

G. G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Monographs and Texts in Physics and Astronomy, Wiley-Interscience, New York, 1972.

9.

B. Iochum and F. W. Shultz, Normal state spaces of Jordan and von Neumann algebras, J. Funct. Analysis 50 (1983), 317-328. MR 0695418

10.

V. F. R. Jones, Subfactors and Knots, CBMS Regional Conference Series in Mathematics, 80, Amer. Math. Soc., Providence, RI, 1991. MR 1134131

11.

R. V. Kadison, A representation theory for commutative topological algebra, Mem. Amer. Math. Soc. 1951, (1951), no. 7. MR 13:360b

12.

G. G. Kasparov, Equivariant -theory and the Novikov conjecture, Invent. Math. 91 (1988), no. 1, 147-201. MR 0918241

13.

G. G. Kasparov and G. Skandalis, Groups acting on buildings, operator -theory, and Novikov's conjecture,-Theory 4 (1991), no. 4, 303-337. MR 1115824

14.

W. Kaup, Jordan algebras and holomorphy, Functional Analysis, Holomorphy, and Approximation Theory (Proc. Sem., Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1978), pp. 341-365, Lecture Notes in Math., 843, Springer, Berlin, 1981. MR 0610837

15.

N. P. Landsman, Quantization as a functor, Quantization, Poisson Brackets and Beyond (Manchester, 2001), pp. 9-24, Contemp. Math. 315, Amer. Math. Soc., Providence, RI, 2002. MR 1958827

16.

N. C. Phillips, Continuous-trace C*-algebras not isomorphic to their opposite algebras, Internat. J. Math. 12 (2001), no. 3, 263-275. MR 1841515

17.

A. Rodríguez-Palacios, Jordan structures in analysis, Jordan Algebras (Oberwolfach, 1992), pp. 97-186, de Gruyter, Berlin, 1994. MR 1293318

18.

R. M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, Chicago Lectures in Physics, University of Chicago Press, Chicago, IL, 1994. MR 1302174