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  • Leibniz A_algebras

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  • https://doi.org/10.2478/cm-2020-0013

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Leibniz A-algebras

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Leibniz A-algebras. / Towers, David.
In: Communications in Mathematics, Vol. 28, No. 2, 11.10.2020, p. 103-121.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Towers, D 2020, 'Leibniz A-algebras', Communications in Mathematics, vol. 28, no. 2, pp. 103-121. https://doi.org/10.2478/cm-2020-0013

APA

Towers, D. (2020). Leibniz A-algebras. Communications in Mathematics, 28(2), 103-121. https://doi.org/10.2478/cm-2020-0013

Vancouver

Towers D. Leibniz A-algebras. Communications in Mathematics. 2020 Oct 11;28(2):103-121. Epub 2020 Sept 17. doi: 10.2478/cm-2020-0013

Author

Towers, David. / Leibniz A-algebras. In: Communications in Mathematics. 2020 ; Vol. 28, No. 2. pp. 103-121.

Bibtex

@article{f100852048a841a899b1e06e493738cc,
title = "Leibniz A-algebras",
abstract = "A finite-dimensional Lie algebra is called an A-algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras.",
keywords = "Lie algebras, Leibniz algebras, $A$-algebras, Frattini ideal, solvable, nilpotent, completely solvable, metabelian, monolithic, cyclic Leibniz algebras",
author = "David Towers",
year = "2020",
month = oct,
day = "11",
doi = "10.2478/cm-2020-0013",
language = "English",
volume = "28",
pages = "103--121",
journal = "Communications in Mathematics",
issn = "2336-1298",
publisher = "de Gruyter",
number = "2",

}

RIS

TY - JOUR

T1 - Leibniz A-algebras

AU - Towers, David

PY - 2020/10/11

Y1 - 2020/10/11

N2 - A finite-dimensional Lie algebra is called an A-algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras.

AB - A finite-dimensional Lie algebra is called an A-algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras.

KW - Lie algebras

KW - Leibniz algebras

KW - $A$-algebras

KW - Frattini ideal

KW - solvable

KW - nilpotent

KW - completely solvable

KW - metabelian

KW - monolithic

KW - cyclic Leibniz algebras

U2 - 10.2478/cm-2020-0013

DO - 10.2478/cm-2020-0013

M3 - Journal article

VL - 28

SP - 103

EP - 121

JO - Communications in Mathematics

JF - Communications in Mathematics

SN - 2336-1298

IS - 2

ER -