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On the subalgebra lattice of a restricted Lie algebra

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On the subalgebra lattice of a restricted Lie algebra. / Paez-Guillan, Pilar; Siciliano, Salvatore; Towers, David.
In: Linear Algebra and its Applications, Vol. 660, 01.03.2023, p. 47-65.

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

Harvard

Paez-Guillan, P, Siciliano, S & Towers, D 2023, 'On the subalgebra lattice of a restricted Lie algebra', Linear Algebra and its Applications, vol. 660, pp. 47-65. https://doi.org/10.1016/j.laa.2022.12.004

APA

Paez-Guillan, P., Siciliano, S., & Towers, D. (2023). On the subalgebra lattice of a restricted Lie algebra. Linear Algebra and its Applications, 660, 47-65. https://doi.org/10.1016/j.laa.2022.12.004

Vancouver

Paez-Guillan P, Siciliano S, Towers D. On the subalgebra lattice of a restricted Lie algebra. Linear Algebra and its Applications. 2023 Mar 1;660:47-65. Epub 2022 Dec 13. doi: 10.1016/j.laa.2022.12.004

Author

Paez-Guillan, Pilar ; Siciliano, Salvatore ; Towers, David. / On the subalgebra lattice of a restricted Lie algebra. In: Linear Algebra and its Applications. 2023 ; Vol. 660. pp. 47-65.

Bibtex

@article{b204886adc7e4fcc918151dd390ce86c,
title = "On the subalgebra lattice of a restricted Lie algebra",
abstract = "In this paper we study the lattice of restricted subalgebras of a restricted Lie algebra. In particular, we consider those algebras in which this lattice is dually atomistic, lower or upper semimodular, or in which every restricted subalgebra is a quasi-ideal. The fact that there are one-dimensional subalgebras which are not restricted results in some of these conditions being weaker than for the corresponding conditions in the non-restricted case.",
keywords = "Restricted Lie algebra, Restricted subalgebra, Frattini p-ideal, Dually atomistic, Restricted quasi-ideal, Lower semimodular, Upper semimodular, J-algebra, Supersolvable",
author = "Pilar Paez-Guillan and Salvatore Siciliano and David Towers",
year = "2023",
month = mar,
day = "1",
doi = "10.1016/j.laa.2022.12.004",
language = "English",
volume = "660",
pages = "47--65",
journal = "Linear Algebra and its Applications",
issn = "0024-3795",
publisher = "Elsevier Inc.",

}

RIS

TY - JOUR

T1 - On the subalgebra lattice of a restricted Lie algebra

AU - Paez-Guillan, Pilar

AU - Siciliano, Salvatore

AU - Towers, David

PY - 2023/3/1

Y1 - 2023/3/1

N2 - In this paper we study the lattice of restricted subalgebras of a restricted Lie algebra. In particular, we consider those algebras in which this lattice is dually atomistic, lower or upper semimodular, or in which every restricted subalgebra is a quasi-ideal. The fact that there are one-dimensional subalgebras which are not restricted results in some of these conditions being weaker than for the corresponding conditions in the non-restricted case.

AB - In this paper we study the lattice of restricted subalgebras of a restricted Lie algebra. In particular, we consider those algebras in which this lattice is dually atomistic, lower or upper semimodular, or in which every restricted subalgebra is a quasi-ideal. The fact that there are one-dimensional subalgebras which are not restricted results in some of these conditions being weaker than for the corresponding conditions in the non-restricted case.

KW - Restricted Lie algebra

KW - Restricted subalgebra

KW - Frattini p-ideal

KW - Dually atomistic

KW - Restricted quasi-ideal

KW - Lower semimodular

KW - Upper semimodular

KW - J-algebra

KW - Supersolvable

U2 - 10.1016/j.laa.2022.12.004

DO - 10.1016/j.laa.2022.12.004

M3 - Journal article

VL - 660

SP - 47

EP - 65

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

ER -