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

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A Bruhat decomposition for subgroups containing the group of diagonal matrices. II. / Vavilov, N. A.

In: Journal of Soviet Mathematics, Vol. 27, No. 4, 11.1984, p. 2865-2874.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{8d1556ddc65e491794208c14e65e2cbe,

title = "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[Figure not available: see fulltext.] such that[Figure not available: see fulltext.]. 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)",

author = "Vavilov, {N. A.}",

year = "1984",

month = nov,

doi = "10.1007/BF01410740",

language = "English",

volume = "27",

pages = "2865--2874",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "4",

}

RIS

TY - JOUR

T1 - A Bruhat decomposition for subgroups containing the group of diagonal matrices. II

AU - Vavilov, N. A.

PY - 1984/11

Y1 - 1984/11

N2 - 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[Figure not available: see fulltext.] such that[Figure not available: see fulltext.]. 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)

AB - 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[Figure not available: see fulltext.] such that[Figure not available: see fulltext.]. 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)

UR - http://www.scopus.com/inward/record.url?scp=34250136407&partnerID=8YFLogxK

U2 - 10.1007/BF01410740

DO - 10.1007/BF01410740

M3 - Article

AN - SCOPUS:34250136407

VL - 27

SP - 2865

EP - 2874

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

ER -

ID: 76483954