Equality of Linear and Symplectic Orbits

Details Equality of Linear and Symplectic Orbits Equality of Linear and Symplectic Orbits

2011-08-05

arxiv.org/abs/1108.1288v1

Mathematics

Commutative Algebra

23 pages

Scientific paper

It is shown that the set of orbits of the action of the elementary symplectic transvection group on all unimodular elements of a symplectic module over a commutative ring of characteristic not 2 is identical with the set of orbits of the action of the corresponding elementary transvection group. This result is used to get improved injective stability estimates for $K_1$ of the symplectic transvection group over a non-singular affine algebras.

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