Unbounded derivations of group 𝐶*-algebras

Lance, Christopher; Niknam, Assadollah

doi:10.1090/S0002-9939-1976-0428051-8

Unbounded derivations of group $C^*$-algebras
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by Christopher Lance and Assadollah Niknam

Proc. Amer. Math. Soc. 61 (1976), 310-314

DOI: https://doi.org/10.1090/S0002-9939-1976-0428051-8

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Abstract:

We describe a construction which yields unbounded derivations and strongly continuous one-parameter automorphism groups of certain group ${C^{\ast }}$-algebras. As an application, we show that a simple ${C^{\ast }}$-algebra can have an automorphism group which is not approximately inner.

References

Ola Bratteli and Derek W. Robinson, Unbounded derivations of $C^{\ast }$-algebras, Comm. Math. Phys. 42 (1975), 253–268. MR 377526, DOI 10.1007/BF01608976
Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173
Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto-London, 1969. MR 0251549
Robert T. Powers, Simplicity of the $C^{\ast }$-algebra associated with the free group on two generators, Duke Math. J. 42 (1975), 151–156. MR 374334
Robert T. Powers and Shôichirô Sakai, Existence of ground states and KMS states for approximately inner dynamics, Comm. Math. Phys. 39 (1974/75), 273–288. MR 359623, DOI 10.1007/BF01705375
Robert T. Powers and Shôichirô Sakai, Unbounded derivations in operator algebras, J. Functional Analysis 19 (1975), 81–95. MR 0383093, DOI 10.1016/0022-1236(75)90007-5
Shôichirô Sakai, On one-parameter subgroups of $^*$-automorphisms on operator algebras and the corresponding unbounded derivations, Amer. J. Math. 98 (1976), no. 2, 427–440. MR 412824, DOI 10.2307/2373896
Shôichirô Sakai, On commutative normal $^*$-derivations. II, J. Functional Analysis 21 (1976), no. 2, 203–208. MR 0420287, DOI 10.1016/0022-1236(76)90078-1