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On the mapping torus of an automorphism


Author: William L. Paschke
Journal: Proc. Amer. Math. Soc. 88 (1983), 481-485
MSC: Primary 46L40
DOI: https://doi.org/10.1090/S0002-9939-1983-0699418-1
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?)

  • [1] A. Connes, An analogue of the Thom isomorphism for crossed products of a $ {C^ * }$-algebra by an action of $ R$, Advances in Math. 39 (1981), 31-55. MR 605351 (82j:46084)
  • [2] J. Cuntz, $ K$-theory for certain $ {C^ * }$-algebras. II, J. Operator Theory 5 (1981), 101-108. MR 613050 (84k:46053)
  • [3] M. Pimsner and D. Voiculescu, Exact sequences for $ K$-groups and Ext-groups of certain cross-products $ {C^ * }$-algebras, J. Operator Theory 4 (1980), 93-118. MR 587369 (82c:46074)
  • [4] J. Taylor, Banach algebras and topology, Algebras in Analysis (J. Williamson, editor), Academic Press, New York, 1975. MR 0417789 (54:5837)

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DOI: https://doi.org/10.1090/S0002-9939-1983-0699418-1
Article copyright: © Copyright 1983 American Mathematical Society

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