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K1 of Exact Categories by Mirror Image Sequences

Published online by Cambridge University Press:  19 April 2012

Clayton Sherman
Clayton Sherman*
Affiliation:
Department of Mathematics, Missouri State University, Springfield, MO 65897, USAcsherman@missouristate.edu
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Abstract

We establish a presentation for K1 of any small exact category P, based on the notion of “mirror image sequence,” originally introduced by Grayson in 1979; as part of the proof, we show that every element of K1(P) arises from a mirror image sequence. This provides an alternative to Nenashev's presentation in terms of “double short exact sequences.”

Keywords

Algebraic K-theoryK1double short exact sequencemirror image sequencePrimary 19D99
Type
Research Article
Information
Journal of K-Theory , Volume 11 , Issue 1 , February 2013 , pp. 155 - 181
Copyright
Copyright © ISOPP 2012

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References

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