CUBO A Mathematical Journal Vol.14, N^o02, (183-196). June 2012

 

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K-theory for the C*-algebras of continuous functions on certain homogeneous spaces in semi-simple Lie groups

Takahiro Sudo

Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus, Senbaru 1, Nishihara, Okinawa 903-0213, Japan

email:sudo@math.u-ryukyu.ac.jp

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ABSTRACT

We study K-theory for thealgebras of all continuous functions on certain homogeneous spaces in the semi-simple connected Lie groups by the discrete subgroups , mainly. As a byproduct, we also consider a certain nilpotent case similarly.

Keywords and Phrases: C*-algebra, K-theory, homogeneous space, semi-simple Lie group, discrete subgroup.

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RESUMEN

Estudiamos la K-teoría para las álgebras de todas las funciones continuas sobre ciertos espacios homogeneos, principalmente en los grupos de Lie conexos semi- simples y subgrupos discretos . Como subproducto consideramos un caso nilpotente en forma anáaloga.

2000 AMS Mathematics Subject Classification: Primary 46L80, 22D25, 22E15.

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References

[1] B. Blaokadar, K-theory for Operator Algebras, SecondEdition, Cambridge, (1998).

[2] T. Natsijme, On , J. Operator Theory 13 (1985), 103-118.

[3] T. Sudo, K-theory of continuous fields of quantum tori, Nihonkai Math. J. 15 (2004), No.2, 141-152.

[4] C. Soule, The cohomology of , Topology, 17 (1978), 1-22.

[5] N. E. Wegge-Olsen, K-theory and algebras, Oxford Univ. Press, 1993.

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Received: July 2011. Revised: December 2011.