Abstract
Since Powers ([9]) proved that the reduced C*-algebra of the free group on two generators C *r (F2) is simple with unique trace, several other classes consisting of discrete groups G such that C *r (G) is simple with unique trace have been produced (see e.g. [1], [4]).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Akemann, C.A.; Lee, T.Y.: Some simple C*-algebra associated with free groups, Indiana Univ. Math. J. 29(1980), 505–511.
Akemann, C.A.; Ostrand, P.: Computing norms in group C*-algebras, Amer. J. Math. 98(1976), 1015–1047.
Boca, F.; Nit̹ică, V.: Combinatorial properties of groups and simple C*-algebras with a unique trace, J. Operator Theory 20(1988), 183–196.
de la Harpe, P.: Reduced C*-algebras of discrete groups which are simple with a unique trace, in Operator algebras and their connections with topology and ergodic theory, Lecture Notes in Math., vol.1132, Springer-Verlag, 1983, pp. 230–253.
Lyndon, R.; Schupp, P.: Combinatorial group theory, Springer-Verlag, 1977.
Magnus, W.; Karrass, A.; Solitar, D.: Combinatorial group theory (Russian), Nauka, 1974.
Murray, F.; von Neumann, J.: Rings of operators. IV, Ann. of Math. 44(1943), 716–808.
Paschke, W.; Salinas, N.: C*-algebras associated with free products of groups, Pacific J. Math. 82(1979), 211–221.
Powers, R.: Simplicity of the C*-algebras associated with the free group on two generators, Duke Math. J. 42(1975), 151–156.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Birkhäuser Verlag Basel
About this chapter
Cite this chapter
Boca, F., Nit̹ică, V. (1990). Extensions of Groups and Simple C*-Algebras. In: Helson, H., Sz.-Nagy, B., Vasilescu, FH., Arsene, G. (eds) Linear Operators in Function Spaces. Operator Theory: Advances and Applications, vol 43. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7250-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7250-8_7
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7252-2
Online ISBN: 978-3-0348-7250-8
eBook Packages: Springer Book Archive