Generalized commutator formulas

R. Hazrat; Z. Zhang

doi:10.1080/00927871003738964

Generalized commutator formulas

R. Hazrat, Z. Zhang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Queen's University Belfast

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

23 Citations (Scopus)

Abstract

Let A be an algebra which is a direct limit of module finite algebras over a commutative ring R with 1. Let I, J be two-sided ideals of A, GL_n(A, I) the principal congruence subgroup of level I in GL_n(A), and E_n(A, I) the relative elementary subgroup of level I. Using Bak's localization-patching method, we prove the commutator formula.

Original language	English
Pages (from-to)	1441-1454
Number of pages	14
Journal	Communications in Algebra
Volume	39
Issue number	4
DOIs	https://doi.org/10.1080/00927871003738964
Publication status	Published - Apr 2011

Keywords

Congruence subgroups
Elementary subgroup
General linear group
Localization and patching
Normal structure
Sandwich classification theorems

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10.1080/00927871003738964

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abstract = "Let A be an algebra which is a direct limit of module finite algebras over a commutative ring R with 1. Let I, J be two-sided ideals of A, GLn(A, I) the principal congruence subgroup of level I in GLn(A), and En(A, I) the relative elementary subgroup of level I. Using Bak's localization-patching method, we prove the commutator formula.",

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AB - Let A be an algebra which is a direct limit of module finite algebras over a commutative ring R with 1. Let I, J be two-sided ideals of A, GLn(A, I) the principal congruence subgroup of level I in GLn(A), and En(A, I) the relative elementary subgroup of level I. Using Bak's localization-patching method, we prove the commutator formula.

KW - Congruence subgroups

KW - Elementary subgroup

KW - General linear group

KW - Localization and patching

KW - Normal structure

KW - Sandwich classification theorems

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DO - 10.1080/00927871003738964

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VL - 39

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EP - 1454

JO - Communications in Algebra

JF - Communications in Algebra

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ER -

Generalized commutator formulas

Abstract

Keywords

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