Geodesic
A Simple C*-Algebra Generated by Two Finite-Order Unitaries
Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 867-880

Voir la notice de l'article provenant de la source Cambridge University Press

We present an example which illustrates several peculiar phenomena that may occur in the theory of C*-algebras. In particular, we show that a C*-subalgebra of a nuclear (amenable) C*-algebra need not be nuclear (amenable).The central object of this paper is a pair of abstract unitary matrices, acting on a common Hilbert space. For an explicit construction, we may decompose an infinite-dimensional Hilbert space H into H = H0 ⴲ H1 , H 1 = H α ⴲ H β with dim H 0 = dim H 1 = dim H α = dim H β, letting u, v Є B(H) be any two unitary operators such that and u2 = 1, v3 = 1. Whereas many choices of u, v are possible, it might be surprising to see that C*(u, v), the C*-algebra generated by u and v, is algebraically unique; namely, if (u1,V1) is another pair of such unitaries, then C*(u, v) is canonically *-isomorphic with C*(u 1, v 1) (Theorem 2.6). 
Choi, Man-Duen. A Simple C*-Algebra Generated by Two Finite-Order Unitaries. Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 867-880. doi: 10.4153/CJM-1979-082-4
@article{10_4153_CJM_1979_082_4,
     author = {Choi, Man-Duen},
     title = {A {Simple} {C*-Algebra} {Generated} by {Two} {Finite-Order} {Unitaries}},
     journal = {Canadian journal of mathematics},
     pages = {867--880},
     year = {1979},
     volume = {31},
     number = {4},
     doi = {10.4153/CJM-1979-082-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-082-4/}
}
TY  - JOUR
AU  - Choi, Man-Duen
TI  - A Simple C*-Algebra Generated by Two Finite-Order Unitaries
JO  - Canadian journal of mathematics
PY  - 1979
SP  - 867
EP  - 880
VL  - 31
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-082-4/
DO  - 10.4153/CJM-1979-082-4
ID  - 10_4153_CJM_1979_082_4
ER  - 
%0 Journal Article
%A Choi, Man-Duen
%T A Simple C*-Algebra Generated by Two Finite-Order Unitaries
%J Canadian journal of mathematics
%D 1979
%P 867-880
%V 31
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-082-4/
%R 10.4153/CJM-1979-082-4
%F 10_4153_CJM_1979_082_4

[1] 1. Akemann, C. A. and Ostrand, P. A., Computing norms in group C*-algebras, Amer. J. Math. 98 (1976), 1015–1047. Google Scholar

[2] 2. Anderson, J., A C*-algebra A for which Ext A is not a group, Ann. of Math. 107 (1978), 455–458. Google Scholar

[3] 3. Apostal, C., Foias, C., and Voiculescu, D., Some results on non-quasi-triangular operators, IV, Rev. Roumaine Math. Pures Appl. 18 (1973), 487–514. Google Scholar

[4] 4. Bunce, J., Characterizations of amenable and strongly amenable C*''-algebras, Pacific J. Math. 43 (1972), 563–572. Google Scholar

[5] 5. Bunce, J., Finite operators and amenable C*-algebras, Proc. Amer. Math. Soc. 56 (1976), 145–151. Google Scholar

[6] 6. Bunce, J. and Paschke, W. L., Quasi-expectations and amenable von Neumann algebras, Proc. Amer. Math. Soc. 71 (1978), 232–236. Google Scholar

[7] 7. Choi, M. D., A Schwarz inequality for positive linear maps on C*-algebras, I1L J. Math. 18 (1974), 565–574. Google Scholar

[8] 8. Choi, M. D. and Effros, E. G., Injectivity and operator spaces, J. Func. Anal. 24 (1977), 156–209. Google Scholar

[9] 9. Choi, M. D. and Effros, E. G., Nuclear C*-algebras and the approximation property, Amer. J. Math. 100 (1978), 61–79. Google Scholar

[10] 10. Choi, M. D. and Effros, E. G., Separable nuclear C*-algebras and injectivity, Duke Math. J. 43 (1976), 309–322. Google Scholar

[11] 11. Choi, M. D. and Effros, E. G., Nuclear C*-algebras and injectivity: the general case, Indiana U. Math. J. 26 (1977), 443–446. Google Scholar

[12] 12. Choi, M. D. and Effros, E. G., Lifting problems and the cohomology of C*-algcbros, Can. J. Math. 29 (1977), 1092–1111. Google Scholar

[13] 13. Connes, A., On the cohomology of operator algebras, J. Func. Anal. 28 (1978), 248–253. Google Scholar

[14] 14. Cnntz, J.: Simple C*-algebras generated by isometrics, Commun. Math. Phys. 57 (1977), 173–185. Google Scholar

[15] 15. Effros, E. G., Aspects of non-commutative order , Notes for a lecture given at the Second U.S.-Japan Seminar on C*-algebras and Applications to Physics, 1977. Google Scholar

[16] 16. Johnson, B. E., Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972). Google Scholar

[17] 17. Lance, E. C., On nuclear C*-algebras, J. Func. Anal. 12 (1973) 157–176. Google Scholar

[18] 18. Powers, R. T., Simplicity of the C*-algebra associated with the free group on two generators, Duke Math. J. 42 (1975), 151–156. Google Scholar

[19] 19. Rosenberg, J., Amenability of cross products of C*-algebras, Comm. Math. Phys. 57 (1977), 187–191. Google Scholar

[20] 20. Stinespring, W. F., Positive functions on C*-algebras, Proc. Amer. Math. Soc. 6 (1955), 211–216. Google Scholar

[21] 21. Takesaki, M., On the crossnorm of the direct product of C*-algebras, Tôhoku Math. J. 16 (1964), 111–122. Google Scholar

[22] 22. Thayer, F. J., Quasi-diagonal C*-algebras, J. Func. Anal. 25 (1977), 50–57. Google Scholar

[23] 23. Tomiyama, J., Tensor products and projections of norm one in von Neumann algebras, Lecture Notes, Univ. of Copenhagen, 1970. Google Scholar

[24] 24. Wassermann, S., On tensor products of certain group C*-algebras, J. Func. Anal. 28 (1976), 239–254. Google Scholar

Cité par Sources :