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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the mapping torus of an automorphism


Author: William L. Paschke
Journal: Proc. Amer. Math. Soc. 88 (1983), 481-485
MSC: Primary 46L40
MathSciNet review: 699418
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Abstract: Let $ \rho $ be an automorphism of a $ {C^ * }$-algebra $ A$. The mapping torus $ {T_\rho }(A)$ is the $ {C^ * }$-algebra of $ A$-valued continuous functions $ x$ on $ [0,1]$ satisfying $ x(1) = \rho (x(0))$. Using his Thom isomorphism theorem, A. Connes has shown that the $ K$-groups of $ {T_\rho }(A)$, with indices reversed, are isomorphic to those of the crossed product $ A{ \times _\rho }Z$. We provide here an alternative proof of this fact which gives an explicit description of the isomorphism.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0699418-1
PII: S 0002-9939(1983)0699418-1
Article copyright: © Copyright 1983 American Mathematical Society