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arXiv · 0909.3351

Injective Stability for K_1 of Classical Modules

Rabeya Basu·Ravi A. Rao
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Abstract

In 1994, the second author and W. van der Kallen showed that the injective stabilization bound for K_1 of general linear group is d+1 over a regular affine algebra over a perfect C_1-field, where d is the krull dimension of the base ring and it is finite and at least 2. In this article we prove that the injective stabilization bound for K_1 of the symplectic group is d+1 over a geometrically regular ring containing a field, where d is the stable dimension of the base ring and it is finite and at least 2. Then using the Local-Global Principle for the transvection subgroup of the automorphism group of projective and symplectic modules we show that the injective stabilization bound is d+1 for k_1 of projective and symplectic modules of global rank at least 1 and local rank at least 3 respectively in each of the two cases above.

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Rabeya Basu, Ravi A. Rao. 2009-09-18. Injective Stability for K_1 of Classical Modules. https://arxiv.org/abs/0909.3351

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