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Algebraic K-Theory

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Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 301)

Abstract

The Grothendieck group K 0(A) of a ring A was introduced in the sixties by Grothendieck in order to give a nice formulation of the Riemann-Roch theorem. Then it was recognized that the Grothendieck group is closely related to the abelianization K 1(A) of the general linear group, which had been studied earlier (1949) by J.H.C. Whitehead in his work on simple homotopy. The next step was the discovery of the K 2-group by Milnor in his attempt to understand the Steinberg symbols in arithmetic. At that point these three groups were expected to be part of a family of algebraic K-functors K n defined for all n ≥ 0. After several attempts by different people, Quillen came with a simple construction, the so-called plus-construction, which gives rise to higher algebraic K-theory.

Keywords

Exact Sequence Banach Algebra General Linear Group Chern Character Cyclic Homology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliographical Comments on Chapter 11

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  1. 1.Institut de Recherche Mathématique AvancéeCentre National de la Recherche ScientifiqueStrasbourgFrance

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