2009/09/18 by Rabeya Basu, Basu, Rabeya, Ravi A. Rao +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AC #math.KT
paper · pdf · doi:10.48550/arxiv.0909.3351
12 pages
arxiv created 2009/09/18 · openalex publication_date 2009/09/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1994, the second author and W. van der Kallen showed that the injective stabilization bound for K1 of general linear group is d+1 over a regular affine algebra over a perfect C1-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 K1 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 k1 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.