Journal of K-theory: K-theory and its Applications to Algebra, Geometry, and Topology

Table of Contents - February 2013 - Volume 11, Issue 01  

Research Article

K1 of Exact Categories by Mirror Image Sequences

Clayton Sherman

Department of Mathematics, Missouri State University, Springfield, MO 65897, USA csherman@missouristate.edu

Abstract

We establish a presentation for K 1 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 K 1(P) arises from a mirror image sequence. This provides an alternative to Nenashev's presentation in terms of “double short exact sequences.”

(Received July 27 2011)

Key Words

  • Algebraic K-theory;
  • K 1 ;
  • double short exact sequence;
  • mirror image sequence

Mathematics Subject Classification 2010

  • Primary 19D99