EXTREMALLY RICH GRAPH $C^*$-ALGEBRAS

  • Jeong, J.A (Mathematical Sciences Division Seoul National University)
  • Published : 2000.09.01

Abstract

Graph C*-algebras C*(E) are the universal C*-algebras generated by partial isometries satisfying the Cuntz-Krieger relations determined by directed graphs E, and it is known that a simple graph C*-algebra is extremally rich in sense that it contains enough extreme consider a sufficient condition on a graph for which the associated graph algebra(possibly nonsimple) is extremally rich. We also present examples of nonextremally rich prime graph C*-algebras with finitely many ideals and with real rank zero.

Keywords

References

  1. J. Funct. Anal. v.99 C*-algebras of real rank zero L. G. Brwon;G. K. Pedersen
  2. On the geometry of the unit ball of a C*- algebra L. G. Brown;G. K. Pedersen
  3. J. reine angew. Math. v.469 On the geometry of the unit ball of a C* -algebra L. G. Brown;G. K. Pedersen
  4. The C* -algebras of row-finite graph T. Bates;D. Pask;I. Raeburn;W. Szymanski
  5. Invent. Math. v.63 A class of C* -algebras and topological Markov chains Ⅱ: Reducible chains and the Ext-functor for C* -algebras J. Cuntz
  6. Invent. Math. v.56 A class of C* -algebras and topological Markov chains J. Cuntz;W. Krieger
  7. Pacific J. Math. Stable rank and real rank of graph C* -algebras J. A Jeong;G. H. Park;D. Y. Shin
  8. Pacific J. Math. v.184 Cuntz-Krieger algebras of directed graphs A. Kumjian;D. Pask;I. Raeburn
  9. J. Funct. Anal. v.144 Graphs, groupoids, and Cuntz-Krieger algebras A. Kumjian;D. Pask;I. Raeburn;J. Renault
  10. J. Operator Theory v.38 Extremal richness of multiplier algebras and corona algebras of simple C* -algebras N. S. Larsen;H. Osaka
  11. J. Operator Theory v.26 The λ-function in operator algebras G. K. Pedersen
  12. J. reine angew. Math. v.410 The invertibles are dense in the irrational rotation C* -algebras I. Putnam
  13. Proc. London Math. Soc. v.46 Dimension and stable rank in the K-theory of C* -algebras M. A. Rieffel