## The Ext class of an approximately inner automorphism

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- by Akitaka Kishimoto and Alex Kumjian PDF
- Trans. Amer. Math. Soc.
**350**(1998), 4127-4148 Request permission

## 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

- Bruce Blackadar,
*$K$-theory for operator algebras*, Mathematical Sciences Research Institute Publications, vol. 5, Springer-Verlag, New York, 1986. MR**859867**, DOI 10.1007/978-1-4613-9572-0 - Bruce Blackadar, Ola Bratteli, George A. Elliott, and Alexander Kumjian,
*Reduction of real rank in inductive limits of $C^\ast$-algebras*, Math. Ann.**292**(1992), no. 1, 111–126. MR**1141788**, DOI 10.1007/BF01444612 - Valentin Deaconu,
*A path model for circle algebras*, J. Operator Theory**34**(1995), no. 1, 57–89. MR**1361567** - George A. Elliott,
*On the classification of $C^*$-algebras of real rank zero*, J. Reine Angew. Math.**443**(1993), 179–219. MR**1241132**, DOI 10.1515/crll.1993.443.179 - George A. Elliott and Mikael Rørdam,
*The automorphism group of the irrational rotation $C^*$-algebra*, Comm. Math. Phys.**155**(1993), no. 1, 3–26. MR**1228523** - Ruy Exel,
*The soft torus and applications to almost commuting matrices*, Pacific J. Math.**160**(1993), no. 2, 207–217. MR**1233352** - Ruy Exel and Terry A. Loring,
*Invariants of almost commuting unitaries*, J. Funct. Anal.**95**(1991), no. 2, 364–376. MR**1092131**, DOI 10.1016/0022-1236(91)90034-3 - Jan-Erik Roos,
*Sur les foncteurs dérivés de $\underleftarrow \lim$. Applications*, C. R. Acad. Sci. Paris**252**(1961), 3702–3704 (French). MR**132091** - Jonathan Rosenberg and Claude Schochet,
*The Künneth theorem and the universal coefficient theorem for Kasparov’s generalized $K$-functor*, Duke Math. J.**55**(1987), no. 2, 431–474. MR**894590**, DOI 10.1215/S0012-7094-87-05524-4 - Mikael Rørdam,
*Classification of certain infinite simple $C^*$-algebras*, J. Funct. Anal.**131**(1995), no. 2, 415–458. MR**1345038**, DOI 10.1006/jfan.1995.1095

## Additional Information

**Akitaka Kishimoto**- Affiliation: Department of Mathematics, Hokkaido University, Sapporo 060 Japan
- MR Author ID: 102095
- Email: kishi@math.sci.hokudai.ac.jp
**Alex Kumjian**- Affiliation: Department of Mathematics, University of Nevada, Reno, Nevada 89557
- Email: alex@unv.edu
- Received by editor(s): August 5, 1996
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**350**(1998), 4127-4148 - MSC (1991): Primary 46L40; Secondary 46L80, 46L35
- DOI: https://doi.org/10.1090/S0002-9947-98-02326-5
- MathSciNet review: 1608321