Adams operations for projective modules over group rings
Adams operations for projective modules over group rings
Let R be a commutative ring, G a finite group acting on R, and let k be a natural number which is invertible in R. Generalizing a definition of Kervaire, we construct an Adams operation \psi ^k on the Grothendieck group and on the higher K-theory of projective modules over the twisted group ring RG. To this end, we generalize Atiyah's cyclic power operations and use shuffle products in higher
K-theory. For the Grothendieck group, we show that \psi ^k is multiplicative and that it commutes with base change, with the Cartan homomorphism, and with \psi ^l for any other l which is invertible in R.
55-71
Koeck, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
1997
Koeck, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
Koeck, Bernhard
(1997)
Adams operations for projective modules over group rings.
Mathematical Proceedings of the Cambridge Philosophical Society, 122 (1), .
Abstract
Let R be a commutative ring, G a finite group acting on R, and let k be a natural number which is invertible in R. Generalizing a definition of Kervaire, we construct an Adams operation \psi ^k on the Grothendieck group and on the higher K-theory of projective modules over the twisted group ring RG. To this end, we generalize Atiyah's cyclic power operations and use shuffle products in higher
K-theory. For the Grothendieck group, we show that \psi ^k is multiplicative and that it commutes with base change, with the Cartan homomorphism, and with \psi ^l for any other l which is invertible in R.
More information
Published date: 1997
Identifiers
Local EPrints ID: 478857
URI: http://eprints.soton.ac.uk/id/eprint/478857
ISSN: 0305-0041
PURE UUID: f101a317-924f-44b5-b484-b856f395fd90
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Date deposited: 11 Jul 2023 17:08
Last modified: 17 Mar 2024 02:53
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