Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Author: K. R. Goodearl
Title: Partially ordered abelian groups with interpolation
Additional book information: Mathematical Surveys and Monographs, number 20, American Mathematical Society, Providence, R.I., 1986, xxii + 336 pp., ISBN 0-8218-1520-2.

References [Enhancements On Off] (What's this?)

  • 1. G. Birkhoff, Lattice-ordered groups, Ann. of Math. (2) 43 (1942), 298-331. MR 6550
  • 2. Ola Bratteli, George A. Elliott, and Akitaka Kishimoto, The temperature state space of a 𝐶*-dynamical system. II, Ann. of Math. (2) 123 (1986), no. 2, 205–263. MR 835762, https://doi.org/10.2307/1971271
  • 3. A. Connes, Non commutative differential geometry, Proceedings of Arbeitstagung 1987 (F. Hirzebruch, ed. ), Max Planck Institute, Univ. of Bonn.
  • 4. Joachim Cuntz and Wolfgang Krieger, Topological Markov chains with dicyclic dimension groups, J. Reine Angew. Math. 320 (1980), 44–51. MR 592141, https://doi.org/10.1515/crll.1980.320.44
  • 5. Edward G. Effros, Dimensions and 𝐶*-algebras, CBMS Regional Conference Series in Mathematics, vol. 46, Conference Board of the Mathematical Sciences, Washington, D.C., 1981. MR 623762
  • 6. Edward G. Effros, David E. Handelman, and Chao Liang Shen, Dimension groups and their affine representations, Amer. J. Math. 102 (1980), no. 2, 385–407. MR 564479, https://doi.org/10.2307/2374244
  • 7. Edward G. Effros and Chao Liang Shen, Approximately finite 𝐶*-algebras and continued fractions, Indiana Univ. Math. J. 29 (1980), no. 2, 191–204. MR 563206, https://doi.org/10.1512/iumj.1980.29.29013
  • 8. G. A. Elliott, On the classification of inductive limits of sequences of semisimple finite-dimensional algebras, J. Algebra 38 (1976), 29-44. MR 397420
  • 9. George A. Elliott, A property of totally ordered abelian groups, C. R. Math. Rep. Acad. Sci. Canada 1 (1978/79), no. 2, 63–66. MR 519524
  • 10. George A. Elliott, On totally ordered groups, and 𝐾₀, Ring theory (Proc. Conf., Univ. Waterloo, Waterloo, 1978) Lecture Notes in Math., vol. 734, Springer, Berlin, 1979, pp. 1–49. MR 548122
  • 11. L. Fuchs, Riesz groups, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 19 (1965), 1-34. MR 180609
  • 12. David E. Handelman, Positive polynomials, convex integral polytopes, and a random walk problem, Lecture Notes in Mathematics, vol. 1282, Springer-Verlag, Berlin, 1987. MR 914972
  • 13. V. F. R. Jones, Braid groups, Hecke algebras and type 𝐼𝐼₁ factors, Geometric methods in operator algebras (Kyoto, 1983) Pitman Res. Notes Math. Ser., vol. 123, Longman Sci. Tech., Harlow, 1986, pp. 242–273. MR 866500
  • 14. A. Lazar and J. Lindenstrauss, Banach spaces whose duals are L, Acta Math. 126 (1971), 165-193. MR 291771
  • 15. Daniele Mundici, Farey stellar subdivisions, ultrasimplicial groups, and 𝐾₀ of AF 𝐶*-algebras, Adv. in Math. 68 (1988), no. 1, 23–39. MR 931170, https://doi.org/10.1016/0001-8708(88)90006-0
  • 16. Adrian Ocneanu, Quantized groups, string algebras and Galois theory for algebras, Operator algebras and applications, Vol. 2, London Math. Soc. Lecture Note Ser., vol. 136, Cambridge Univ. Press, Cambridge, 1988, pp. 119–172. MR 996454
  • 17. M. Pimsner and D. Voiculescu, Imbedding the irrational rotation 𝐶*-algebra into an AF-algebra, J. Operator Theory 4 (1980), no. 2, 201–210. MR 595412
  • 18. Jean Renault, A groupoid approach to 𝐶*-algebras, Lecture Notes in Mathematics, vol. 793, Springer, Berlin, 1980. MR 584266
  • 19. F. Riesz, Sur quelques notions fondamentales dans la théorie générale des opérations linéaires, Ann. of Math. (2) 41 (1940), 174-206. MR 902
  • 20. Chao Liang Shen, On the classification of the ordered groups associated with the approximately finite-dimensional 𝐶*-algebras, Duke Math. J. 46 (1979), no. 3, 613–633. MR 544249
  • 21. A. M. Vershik and S. V. Kerov, Locally semisimple algebras, combinatorial theory, and the K, J. Soviet Math. 38 (1987), 1701- 1733.

Review Information:

Reviewer: George A. Elliott
Journal: Bull. Amer. Math. Soc. 21 (1989), 200-204
DOI: https://doi.org/10.1090/S0273-0979-1989-15822-9
American Mathematical Society