Whitehead groups of localizations and the endomorphism class group
Copyright policy )Whitehead groups of localizations and the endomorphism class group
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,��) where P is a finitely generated projective A-module and ��:P \to P is an endomorphism. This invariant determines (P,��) 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.
21 pages, LaTeX, with minor revisions
- University of California, Riverside United States
Algebra and Number Theory, 18F25, K-Theory and Homology (math.KT), Mathematics - Rings and Algebras, Whitehead groups and \(K_1\), 37C27, localization, Rings and Algebras (math.RA), local augmentation, Mathematics - K-Theory and Homology, Whitehead groups, FOS: Mathematics, 16S34, 18F25; 16S10; 16S34; 37C27, 16S10
Algebra and Number Theory, 18F25, K-Theory and Homology (math.KT), Mathematics - Rings and Algebras, Whitehead groups and \(K_1\), 37C27, localization, Rings and Algebras (math.RA), local augmentation, Mathematics - K-Theory and Homology, Whitehead groups, FOS: Mathematics, 16S34, 18F25; 16S10; 16S34; 37C27, 16S10
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