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Zap. Nauchn. Sem. LOMI, 1982 Volume 114, Pages 50–61 (Mi znsl1766)

This article is cited in 7 papers

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

N. A. Vavilov


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 $\mathfrak J$ is the Jacobson radical of $R$, and $B(\mathfrak J)$ is a subgroup of $GL(n,R)$ consisting of the matrices $a=(a_{ij})$ such that $a_{ij}\in\mathfrak J $ for$i>j$. If a matrix $a\in B(\mathfrak J)$ is represented in the form $a=udv$, where $u$ is upper unitriangular, $d$ is diagonal, and $v$ is lower unitriangular, then $u,v\in\langle D,ada^{-1}\rangle$, where $D=D(n,R)$ is the group of diagonal matrices. In particular, $D$ is abnormal in $B(\mathfrak J)$.

UDC: 519.46


 English version:
Journal of Soviet Mathematics, 1984, 27:4, 2865–2874

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