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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.

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

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Article copyright: © Copyright 1983 American Mathematical Society