Bulletin of the American Mathematical Society

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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.

Garrett Birkhoff, Lattice, ordered groups, Ann. of Math. (2) 43 (1942), 298–331. MR 6550, DOI 10.2307/1968871

Ola Bratteli, George A. Elliott, and Akitaka Kishimoto, The temperature state space of a $C^\ast$-dynamical system. II, Ann. of Math. (2) 123 (1986), no. 2, 205–263. MR 835762, DOI 10.2307/1971271

3.

A. Connes, Non commutative differential geometry, Proceedings of Arbeitstagung 1987 (F. Hirzebruch, ed. ), Max Planck Institute, Univ. of Bonn.

Joachim Cuntz and Wolfgang Krieger, Topological Markov chains with dicyclic dimension groups, J. Reine Angew. Math. 320 (1980), 44–51. MR 592141, DOI 10.1515/crll.1980.320.44

Edward G. Effros, Dimensions and $C^{\ast }$-algebras, CBMS Regional Conference Series in Mathematics, vol. 46, Conference Board of the Mathematical Sciences, Washington, D.C., 1981. MR 623762

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, DOI 10.2307/2374244

Edward G. Effros and Chao Liang Shen, Approximately finite $C^{\ast }$-algebras and continued fractions, Indiana Univ. Math. J. 29 (1980), no. 2, 191–204. MR 563206, DOI 10.1512/iumj.1980.29.29013

George A. Elliott, On the classification of inductive limits of sequences of semisimple finite-dimensional algebras, J. Algebra 38 (1976), no. 1, 29–44. MR 397420, DOI 10.1016/0021-8693(76)90242-8

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

George A. Elliott, On totally ordered groups, and $K_{0}$, Ring theory (Proc. Conf., Univ. Waterloo, Waterloo, 1978) Lecture Notes in Math., vol. 734, Springer, Berlin, 1979, pp. 1–49. MR 548122

L. Fuchs, Riesz groups, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 19 (1965), 1–34. MR 180609

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, DOI 10.1007/BFb0078909

V. F. R. Jones, Braid groups, Hecke algebras and type $\textrm {II}_1$ 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

A. J. Lazar and J. Lindenstrauss, Banach spaces whose duals are $L_{1}$ spaces and their representing matrices, Acta Math. 126 (1971), 165–193. MR 291771, DOI 10.1007/BF02392030

Daniele Mundici, Farey stellar subdivisions, ultrasimplicial groups, and $K_0$ of AF $C^*$-algebras, Adv. in Math. 68 (1988), no. 1, 23–39. MR 931170, DOI 10.1016/0001-8708(88)90006-0

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

M. Pimsner and D. Voiculescu, Imbedding the irrational rotation $C^{\ast }$-algebra into an AF-algebra, J. Operator Theory 4 (1980), no. 2, 201–210. MR 595412

Jean Renault, A groupoid approach to $C^{\ast }$-algebras, Lecture Notes in Mathematics, vol. 793, Springer, Berlin, 1980. MR 584266

Frédéric Riesz, Sur quelques notions fondamentales dans la théorie générale des opérations linéaires, Ann. of Math. (2) 41 (1940), 174–206 (French). MR 902, DOI 10.2307/1968825

Chao Liang Shen, On the classification of the ordered groups associated with the approximately finite-dimensional $C^{\ast }$-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.

1.

G. Birkhoff, Lattice-ordered groups, Ann. of Math. (2) 43 (1942), 298-331. MR 0006550

2.

O. Bratteli, G. A. Elliott, and A. Kishimoto, The temperature state space of a C*-dynamical system. II, Ann. of Math. (2) 123 (1986), 205-263. MR 835762

3.

A. Connes, Non commutative differential geometry, Proceedings of Arbeitstagung 1987 (F. Hirzebruch, ed. ), Max Planck Institute, Univ. of Bonn.

4.

J. Cuntz and W. Krieger, Topological Markov chains with dicyclic dimension groups, J. Reine Angew. Math. 320 (1980), 44-51. MR 592141

5.

E. G. Effros, Dimensions and C*-algebras, CBMS Regional Conf. Ser. in Math., No. 46, Amer. Math. Soc., Providence, R. I., 1981. MR 623762

6.

E. G. Effros, D. E. Handelman, and C.-L. Shen, Dimension groups and their affine representations, Amer. J. Math. 102 (1980), 385-407. MR 564479

7.

E. G. Effros and C.-L. Shen, Approximately finite C*-algebras and continued fractions, Indiana Univ. Math. J. 29 (1980), 191-204. MR 563206

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.

G. A. Elliott, A property of totally ordered groups, C. R. Math. Rep. Acad. Sci. Canada 1 (1979), 63-66. MR 519524

10.

G. A. Elliott, On totally ordered groups, and K₀, Ring Theory, Waterloo, 1978 (D. Handelman and J. Lawrence, eds. ), Lecture Notes in Math., vol. 734, Springer-Verlag, Berlin and New York, 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.

D. E. Handelman, Positive polynomials, convex integral polytopes, and a random walk problem, Lecture Notes in Math., vol. 1282, Springer-Verlag, Berlin and New York, 1987. MR 914972

13.

V. F. R. Jones, Braid groups, Hecke algebras and type II, Geometric Methods in Operator Algebras (H. Araki and E. G. Effros, eds. ), Longman, London, 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.

D. Mundici, Farey stellar subdivisions, ultrasimplicial groups, and K, Adv. in Math. 68 (1988), 23-39. MR 931170

16.

A. Ocneanu, Quantized groups, string algebras, and Galois theory for algebras, preprint. MR 996454

17.

M. Pimsner and D. Voiculescu, Imbedding the irrational rotation C*-algebra into an AF-algebra, J. Operator Theory 4 (1980), 201-210. MR 595412

18.

J. Renault, A groupoid approach to C*-algebras, Lecture Notes in Math., vol. 793, Springer-Verlag, Berlin and New York, 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.

C.-L. Shen, On the classification of the ordered groups associated with the approximately finite-dimensional C*-algebras, Duke Math. J. 46 (1979), 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.