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Adams operations for projective modules over group rings

Published online by Cambridge University Press:  01 July 1997

BERNHARD KÖCK
BERNHARD KÖCK
Affiliation:
Math. Institut II der Universität Karlsruhe, D-76128 Karlsruhe, Germany e-mail: bk@ma2s2.mathematik.uni-karlsruhe.de
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Abstract

Let R be a commutative ring, Γ a finite group acting on R, and let k∈ℕ be invertible in R. Generalizing a definition of Kervaire, we construct an Adams operation ψk on the Grothendieck group and on the higher K-theory of projective modules over the twisted group ring R#Γ. For this, we generalize Atiyah's cyclic power operations and use shuffle products in higher K-theory. For the Grothendieck group, we show that ψk is multiplicative and that it commutes with base change, with the Cartan homomorphism, and with ψl for any other l which is invertible in R.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 1 , July 1997 , pp. 55 - 71
Copyright
Cambridge Philosophical Society 1997

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