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Elementary symplectic orbits and improved K1-stability

Published online by Cambridge University Press:  10 June 2010

Pratyusha Chattopadhyay  and
Ravi A. Rao
Pratyusha Chattopadhyay
Affiliation:
Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600 113, India, pratyusha@imsc.res.in
Ravi A. Rao
Affiliation:
Tata Institute of Fundamental Research, Dr. Homi Bhabha Road, Navy Nagar, Mumbai 400005, India, ravi@math.tifr.res.in
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Abstract

It is shown that the set of orbits of the action of the elementary symplectic group on all unimodular rows over a commutative ring of characteristic not 2 is identical with the set of orbits of the action of the corresponding elementary general linear group. This result is used to improve injective stability for K1 of the symplectic group over non-singular affine algebras.

Keywords

unimodular rowselementary symplectic group
Type
Research Article
Information
Journal of K-Theory , Volume 7 , Issue 2 , April 2011 , pp. 389 - 403
Copyright
Copyright © ISOPP 2010

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