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GROUPS WITH Aℓ-COMMUTATOR RELATIONS. / Voronetsky, E.

в: St. Petersburg Mathematical Journal, Том 35, № 3, 30.07.2024, стр. 433-443.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Voronetsky, E 2024, 'GROUPS WITH Aℓ-COMMUTATOR RELATIONS', St. Petersburg Mathematical Journal, Том. 35, № 3, стр. 433-443. https://doi.org/10.1090/spmj/1810

APA

Voronetsky, E. (2024). GROUPS WITH Aℓ-COMMUTATOR RELATIONS. St. Petersburg Mathematical Journal, 35(3), 433-443. https://doi.org/10.1090/spmj/1810

Vancouver

Voronetsky E. GROUPS WITH Aℓ-COMMUTATOR RELATIONS. St. Petersburg Mathematical Journal. 2024 Июль 30;35(3):433-443. https://doi.org/10.1090/spmj/1810

Author

Voronetsky, E. / GROUPS WITH Aℓ-COMMUTATOR RELATIONS. в: St. Petersburg Mathematical Journal. 2024 ; Том 35, № 3. стр. 433-443.

BibTeX

@article{ea28d16a43144c65969435da35550dd5,
title = "GROUPS WITH Aℓ-COMMUTATOR RELATIONS",
abstract = "If A is a unital associative ring and ℓ ≥ 2, then the general linear group GL(ℓ, A) has root subgroups Uα and Weyl elements nα for α from the root system of type Aℓ−1. Conversely, if an arbitrary group has such root subgroups and Weyl elements for ℓ ≥ 4 satisfying natural conditions, then there is a way to recover the ring A. A generalization of this result not involving the Weyl elements is proved, so instead of the matrix ring M(ℓ, A), a nonunital associative ring with a well-behaved Peirce decomposition is provided. {\textcopyright} 2024 American Mathematical Society",
keywords = "General linear group, root subgroups",
author = "E. Voronetsky",
note = "Export Date: 4 November 2024",
year = "2024",
month = jul,
day = "30",
doi = "10.1090/spmj/1810",
language = "Английский",
volume = "35",
pages = "433--443",
journal = "St. Petersburg Mathematical Journal",
issn = "1061-0022",
publisher = "American Mathematical Society",
number = "3",

}

RIS

TY - JOUR

T1 - GROUPS WITH Aℓ-COMMUTATOR RELATIONS

AU - Voronetsky, E.

N1 - Export Date: 4 November 2024

PY - 2024/7/30

Y1 - 2024/7/30

N2 - If A is a unital associative ring and ℓ ≥ 2, then the general linear group GL(ℓ, A) has root subgroups Uα and Weyl elements nα for α from the root system of type Aℓ−1. Conversely, if an arbitrary group has such root subgroups and Weyl elements for ℓ ≥ 4 satisfying natural conditions, then there is a way to recover the ring A. A generalization of this result not involving the Weyl elements is proved, so instead of the matrix ring M(ℓ, A), a nonunital associative ring with a well-behaved Peirce decomposition is provided. © 2024 American Mathematical Society

AB - If A is a unital associative ring and ℓ ≥ 2, then the general linear group GL(ℓ, A) has root subgroups Uα and Weyl elements nα for α from the root system of type Aℓ−1. Conversely, if an arbitrary group has such root subgroups and Weyl elements for ℓ ≥ 4 satisfying natural conditions, then there is a way to recover the ring A. A generalization of this result not involving the Weyl elements is proved, so instead of the matrix ring M(ℓ, A), a nonunital associative ring with a well-behaved Peirce decomposition is provided. © 2024 American Mathematical Society

KW - General linear group

KW - root subgroups

UR - https://www.mendeley.com/catalogue/33d67eca-e511-38cc-91ea-77f8c419a577/

U2 - 10.1090/spmj/1810

DO - 10.1090/spmj/1810

M3 - статья

VL - 35

SP - 433

EP - 443

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 3

ER -

ID: 126740538