Subnormal structure of the general linear groups over Banach algebras

Leonid N. Vaserstein

doi:10.1016/0022-4049(88)90146-6

Subnormal structure of the general linear groups over Banach algebras

Leonid N. Vaserstein

Mathematics

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10 Scopus citations

Abstract

Let GL_nA be the group of invertible matrices over a ring A and E_nA the subgroup generated by elementary matrices. In previous papers, the author described all subgroups of GL_nA, n≥3, normalized by E_nA for a few classes of rings A including all Banach algebras A with 1 (in the case n=2, the situation is more complicated). The present paper extends this to a wider class of rings. However, the main goal is to give a complete description of all subnormal subgroups of E_nA for this class of rings including all Banach algebras A with 1.

Original language	English (US)
Pages (from-to)	187-195
Number of pages	9
Journal	Journal of Pure and Applied Algebra
Volume	52
Issue number	1-2
DOIs	https://doi.org/10.1016/0022-4049(88)90146-6
State	Published - May 1988

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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title = "Subnormal structure of the general linear groups over Banach algebras",

abstract = "Let GLnA be the group of invertible matrices over a ring A and EnA the subgroup generated by elementary matrices. In previous papers, the author described all subgroups of GLnA, n≥3, normalized by EnA for a few classes of rings A including all Banach algebras A with 1 (in the case n=2, the situation is more complicated). The present paper extends this to a wider class of rings. However, the main goal is to give a complete description of all subnormal subgroups of EnA for this class of rings including all Banach algebras A with 1.",

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AB - Let GLnA be the group of invertible matrices over a ring A and EnA the subgroup generated by elementary matrices. In previous papers, the author described all subgroups of GLnA, n≥3, normalized by EnA for a few classes of rings A including all Banach algebras A with 1 (in the case n=2, the situation is more complicated). The present paper extends this to a wider class of rings. However, the main goal is to give a complete description of all subnormal subgroups of EnA for this class of rings including all Banach algebras A with 1.

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JO - Journal of Pure and Applied Algebra

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ER -

Subnormal structure of the general linear groups over Banach algebras

Abstract

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