Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The Ext class of an approximately inner automorphism

Authors: Akitaka Kishimoto and Alex Kumjian
Journal: Trans. Amer. Math. Soc. 350 (1998), 4127-4148
MSC (1991): Primary 46L40; Secondary 46L80, 46L35
MathSciNet review: 1608321
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $A$ be a simple unital $A\mathbf{T}$ algebra of real rank zero. It is shown below that the range of the natural map from the approximately inner automorphism group to $KK(A, A)$ coincides with the kernel of the map $KK(A, A) \rightarrow \bigoplus _{i=0}^{1} \operatorname{Hom}(K_i(A), K_i(A))$.

References [Enhancements On Off] (What's this?)

  • [B] B. Blackadar, K-theory for operator algebras, MSRI Publications 5, Springer-Verlag, New York, 1986. MR 88g:46082
  • [BBEK] B. Blackadar, O. Bratteli, G. A. Elliott and A. Kumjian, Reduction of real rank in inductive limits of C*-algebras, Math. Ann. (1992) 111-126. MR 93a:46112
  • [D] V. Deaconu, A path model for circle algebras, J. Operator Theory 34 (1995) 57-89. MR 96m:46113
  • [E] G. A. Elliott, On the classification of C*-algebras of real rank zero, J. Reine Angew. Math. 443 (1993) 179-219. MR 94i:46074
  • [ER] G. A. Elliott and M. Rørdam, The automorphism group of the irrational rotation C*-algebra, Commun. Math. Phys. 155 (1993) 3-26. MR 94j:46059
  • [Ex] R. Exel, The soft torus and applications to almost commuting matrices, Pacific J. Math. 160 (1993) 207-217. MR 94f:46091
  • [EL] R. Exel and T. Loring, Invariants of almost commuting matrices, J. Funct. Anal. 95 (1991) 364-376. MR 92a:46083
  • [Ro] J. E. Roos, Sur les foncteurs dérivés de $\stackrel {\textstyle\lim}{\mbox{$\leftarrow $}}$. Applications, C. R. Acad. Sci. Paris 252 (1961) 3702-3704. MR 24:A1938
  • [RS] J. Rosenberg and C. Schochet, The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K-functor, Duke Math. J. 55 (1987) 431-474. MR 88i:46091
  • [Rø] M. Rørdam, Classification of certain infinite simple C*-algebras, J. Funct. Anal. 131 (1995) 415-458. MR 96e:46080a

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 46L40, 46L80, 46L35

Retrieve articles in all journals with MSC (1991): 46L40, 46L80, 46L35

Additional Information

Akitaka Kishimoto
Affiliation: Department of Mathematics, Hokkaido University, Sapporo 060 Japan

Alex Kumjian
Affiliation: Department of Mathematics, University of Nevada, Reno, Nevada 89557

Received by editor(s): August 5, 1996
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society