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On the subalgebra lattice of a Leibniz algebra

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On the subalgebra lattice of a Leibniz algebra. / Siciliano, Salvatore; Towers, David.
In: Communications in Algebra, Vol. 50, No. 1, 31.01.2022, p. 255-267.

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

Harvard

Siciliano, S & Towers, D 2022, 'On the subalgebra lattice of a Leibniz algebra', Communications in Algebra, vol. 50, no. 1, pp. 255-267. https://doi.org/10.1080/00927872.2021.1956510

APA

Siciliano, S., & Towers, D. (2022). On the subalgebra lattice of a Leibniz algebra. Communications in Algebra, 50(1), 255-267. https://doi.org/10.1080/00927872.2021.1956510

Vancouver

Siciliano S, Towers D. On the subalgebra lattice of a Leibniz algebra. Communications in Algebra. 2022 Jan 31;50(1):255-267. Epub 2021 Aug 2. doi: 10.1080/00927872.2021.1956510

Author

Siciliano, Salvatore ; Towers, David. / On the subalgebra lattice of a Leibniz algebra. In: Communications in Algebra. 2022 ; Vol. 50, No. 1. pp. 255-267.

Bibtex

@article{c8f20d81d4f545c7b9152e41d90282a0,
title = "On the subalgebra lattice of a Leibniz algebra",
abstract = " In this paper we begin to study the subalgebra lattice of a Leibniz algebra. In particular, we deal with Leibniz algebras whose subalgebra lattice is modular, upper semi-modular, lower semi-modular, distributive, or dually atomistic. The fact that a non-Lie Leibniz algebra has fewer one-dimensional subalgebras in general results in a number of lattice conditions being weaker than in the Lie case.",
keywords = "Cyclic, extraspecial Leibniz algebra, Frattini ideal, Lie algebras, lower semi-modular, nilpotent, solvable, supersolvable, upper semi-modular",
author = "Salvatore Siciliano and David Towers",
year = "2022",
month = jan,
day = "31",
doi = "10.1080/00927872.2021.1956510",
language = "English",
volume = "50",
pages = "255--267",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor and Francis Ltd.",
number = "1",

}

RIS

TY - JOUR

T1 - On the subalgebra lattice of a Leibniz algebra

AU - Siciliano, Salvatore

AU - Towers, David

PY - 2022/1/31

Y1 - 2022/1/31

N2 - In this paper we begin to study the subalgebra lattice of a Leibniz algebra. In particular, we deal with Leibniz algebras whose subalgebra lattice is modular, upper semi-modular, lower semi-modular, distributive, or dually atomistic. The fact that a non-Lie Leibniz algebra has fewer one-dimensional subalgebras in general results in a number of lattice conditions being weaker than in the Lie case.

AB - In this paper we begin to study the subalgebra lattice of a Leibniz algebra. In particular, we deal with Leibniz algebras whose subalgebra lattice is modular, upper semi-modular, lower semi-modular, distributive, or dually atomistic. The fact that a non-Lie Leibniz algebra has fewer one-dimensional subalgebras in general results in a number of lattice conditions being weaker than in the Lie case.

KW - Cyclic

KW - extraspecial Leibniz algebra

KW - Frattini ideal

KW - Lie algebras

KW - lower semi-modular

KW - nilpotent

KW - solvable

KW - supersolvable

KW - upper semi-modular

U2 - 10.1080/00927872.2021.1956510

DO - 10.1080/00927872.2021.1956510

M3 - Journal article

VL - 50

SP - 255

EP - 267

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 1

ER -