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elementary symplectic group

Journal of K-Theory (1)

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Elementary symplectic orbits and improved K1-stability
Pratyusha Chattopadhyay, Ravi A. Rao
Journal:

Journal of K-Theory / Volume 7 / Issue 2 / April 2011

Published online by Cambridge University Press:

10 June 2010, pp. 389-403

Print publication:

April 2011
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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.