Whitehead Groups of Localizations and the Endomorphism Class Group
K-Theory and Homology
2007-05-23 v2 Rings and Algebras
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,\alpha) where P is a finitely generated projective A-module and \alpha:P \to P is an endomorphism. This invariant determines (P,\alpha) 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.
Cite
@article{arxiv.math/0209311,
title = {Whitehead Groups of Localizations and the Endomorphism Class Group},
author = {Desmond Sheiham},
journal= {arXiv preprint arXiv:math/0209311},
year = {2007}
}
Comments
21 pages, LaTeX, with minor revisions