Real and stable ranks for certain crossed products of Toeplitz algebras

• Takahiro Sudo ^[1]
  1. [1] University of the Ryukyus

     University of the Ryukyus

     Nishihara Chō, Japón

     
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 12, Nº. 2, 2010, págs. 261-274
• Idioma: inglés
• DOI: 10.4067/S0719-06462010000200016
• Enlaces
  • Texto completo
• Resumen
  • español

    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.

  • English

    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.

• Referencias bibliográficas
  • Beggs, E.J,Evans, D.E. (1991). The real rank of algebras of matrix valued functions. Internat. J. Math. 2. 131-138
  • Blackadar, B. (1998). K-theory for Operator Algebras.
  • Brown, L.G,Pedersen, G.K. (1991). C*-algebras of real rank zero. J. Funct. Anal. 99. 131-149
  • Elhage Hassan, N. (1995). Rangs stables de certaines extensions. J. London Math. Soc. 52. 605-624
  • Elhage Hassan, N. (1995). Rang réel de certaines extensions. Proc. Amer. Math. Soc.. 123. 3067-3073
  • Murphy, G.J. (1990). C*-algebras and Operator theory. Academic Press.
  • Nagisa, M,Osaka, H,Phillips, N.C. (2001). anks of algebras of continuous C*-algebra valued functions. Canad. J. Math. 53. 979-1030
  • Nistor, V. (1987). Stable rank for a certain class of type I C*-algebras. J. Operator Theory. 17. 365-373
  • Pedersen, G.K. (1979). C*-Algebras and their Automorphism Groups. Academic Press.
  • Rieffel, M.A. (1983). Dimension and stable rank in the K-theory of C*-algebras. Proc. London Math. Soc. 46. 301-333
  • Rieffel, M.A. (1987). The homotopy groups of the unitary groups of non-commutative tori. J. Operator Theory. 17. 237-254
  • Rørdam, M. (1995). Classification of certain infinite simple C*-algebras. J. Funct. Anal.. 131. 415-458
  • Sheu, A.J-L. (1987). A cancellation theorem for projective modules over the group C*-algebras of certain nilpotent Lie groups. Canad. J. Math....
  • Sudo, T. (2004). The structure of group C*-algebras of some discrete solvable semi-direct products. Hokkaido Math. J. 587-606
  • Sudo, T. (2007). Real rank estimate by hereditary C*-subalgebras by projections. Math. Scand. 100. 361-367