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Whitehead Groups of Localizations and the Endomorphism Class Group

Desmond Sheiham
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Abstract

We compute the Whitehead groups of the associative rings in a class which includes (twisted) formal power series rings and the augmentation localizations of group rings and polynomial rings. For any associative ring A, we obtain an invariant of a pair (P,α) where P is a finitely generated projective A-module and α:P \to P is an endomorphism. This invariant determines (P,α) up to extensions, yielding a computation of the (reduced) endomorphism class group of A. We also refine the analysis by Pajitnov and Ranicki of the Whitehead group of the Novikov ring.

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Desmond Sheiham. 2004-04-12. Whitehead Groups of Localizations and the Endomorphism Class Group. https://arxiv.org/abs/math/0209311

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