Injective stability for K1 of classical modules

Basu, Rabeya ; Rao, Ravi A. (2010) Injective stability for K1 of classical modules Journal of Algebra, 323 (4). pp. 867-877. ISSN 0021-8693

Full text not available from this repository.

Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.jalgebra.2009.12.012

Abstract

In Rao (1994) [14], the second author and W. van der Kallen showed that the injective stabilization bound for K1 of the 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 which 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 dimension of the base ring which is finite and at least 2. 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.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Regular Ring; Affine Algebra; Projective Modules; K1; K1 Sp
ID Code:107125
Deposited On:26 Dec 2017 11:21
Last Modified:26 Dec 2017 11:21

Repository Staff Only: item control page