Sandwich classification for O 2n+1(R) and U 2n+1(R,Δ) revisited

Abstract

In a recent paper, the author proved that if n 3 is a natural number, R a commutative ring and 2 GLn.R/, then tkl.ij / where i j and k l can be expressed as a product of 8 matrices of the form 1 where 2 En.R/. In this article we prove similar results for the odd-dimensional orthogonal groups O2nC1.R/ and the odd-dimensional unitary groups U2nC1.R; / under the assumption that R is commutative and n 3. This yields new, short proofs of the Sandwich Classification Theorems for the groups O2nC1.R/ and U2nC1.R; /.