CUBO A Mathematical Journal Vol.12, N° 02, (261–274). June 201

Real and stable ranks for certain crossed products of Toeplitz algebras

Takahiro Sudo

Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus, Nishihara, Okinawa 903-0213, Japan email: sudo@math.u-ryukyu.ac.jp

ABSTRACT

We consider the algebraic structure of certain crossed products of the Toeplitz algebra and its tensor products. Using the structure, we estimate the stable rank and real rank of those crossed products. In particular, we obtain a real rank estimate for extensions of C*-algebras.

Key words and phrases: C*-algebra, Crossed products, Stable rank, Real rank, Toeplitz algebra.

RESUMEN

Consideramos la estructura algebraica de ciertos productos cruzados de algebra de Toeplitz y sus productos tensoriales. Usando la estructura estimamos el rango estable y el rango real de estos productos cruzados. En particular, obtenemos una estimativa del rango real para extensiones de C*-algebras.

2000 Math. Subj. Class.: Primary 46L05, 46L80

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Received: March 2009.

Revised: July 2009.