A Bruhat decomposition for subgroups containing the group of diagonal matrices. II

Abstract

This paper is a continuation of RZhMat 1981, 7A438. Suppose R is a commutative ring generated by its group of units R* and there exist such that . Suppose also that ℑ is the Jacobson radical of R, and B(ℑ) is a subgroup of GL(n,R) consisting of the matrices a=(aij) such that aij∃ℑ for i>j. If a matrix a∃B(ℑ) is represented in the form a=udv, where u is upper unitriangular, d is diagonal, and v is lower unitriangular, then u,v∃〈D,aDa−1〉, where D=D(n,R) is the group of diagonal matrices. In particular, D is abnormal in B(ℑ)