On the mapping torus of an automorphism
HTML articles powered by AMS MathViewer
- by William L. Paschke PDF
- Proc. Amer. Math. Soc. 88 (1983), 481-485 Request permission
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
- A. Connes, An analogue of the Thom isomorphism for crossed products of a $C^{\ast }$-algebra by an action of $\textbf {R}$, Adv. in Math. 39 (1981), no. 1, 31–55. MR 605351, DOI 10.1016/0001-8708(81)90056-6
- Joachim Cuntz, $K$-theory for certain $C^{\ast }$-algebras. II, J. Operator Theory 5 (1981), no. 1, 101–108. MR 613050
- M. Pimsner and D. Voiculescu, Exact sequences for $K$-groups and Ext-groups of certain cross-product $C^{\ast }$-algebras, J. Operator Theory 4 (1980), no. 1, 93–118. MR 587369
- J. L. Taylor, Banach algebras and topology, Algebras in analysis (Proc. Instructional Conf. and NATO Advanced Study Inst., Birmingham, 1973) Academic Press, London, 1975, pp. 118–186. MR 0417789
Additional Information
- © Copyright 1983 American Mathematical Society
- 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