On the Cartan Map for Crossed Products and Hopf–Galois Extensions |
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Authors: | Konstantin Ardakov Simon J Wadsley |
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Institution: | 1.School of Mathematical Sciences,University of Nottingham,Nottingham,UK;2.Department of Pure Mathematics and Mathematical Statistics,Centre for Mathematical Sciences,Cambridge,UK |
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Abstract: | We study certain aspects of the algebraic K-theory of Hopf–Galois extensions. We show that the Cartan map from K-theory to
G-theory of such an extension is a rational isomorphism, provided the ring of coinvariants is regular, the Hopf algebra is
finite dimensional and its Cartan map is injective in degree zero. This covers the case of a crossed product of a regular
ring with a finite group and has an application to the study of Iwasawa modules. |
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