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    Rights statement: Copyright Heldermann Verlag 2021

    Accepted author manuscript, 138 KB, PDF document

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

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On certain classes of algebras in which centralizers are ideals

Research output: Contribution to Journal/Magazine › Journal article

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On certain classes of algebras in which centralizers are ideals. / Towers, David; Saha, Ripan.
In: Journal of Lie Theory, Vol. 31, No. 4, 23.11.2021, p. 991-1002.

Research output: Contribution to Journal/Magazine › Journal article

Harvard

Towers, D & Saha, R 2021, 'On certain classes of algebras in which centralizers are ideals', Journal of Lie Theory, vol. 31, no. 4, pp. 991-1002. <https://www.heldermann.de/JLT/JLT31/JLT314/jlt31050.htm>

APA

Towers, D., & Saha, R. (2021). On certain classes of algebras in which centralizers are ideals. Journal of Lie Theory, 31(4), 991-1002. https://www.heldermann.de/JLT/JLT31/JLT314/jlt31050.htm

Vancouver

Towers D, Saha R. On certain classes of algebras in which centralizers are ideals. Journal of Lie Theory. 2021 Nov 23;31(4):991-1002.

Author

Towers, David ; Saha, Ripan. / On certain classes of algebras in which centralizers are ideals. In: Journal of Lie Theory. 2021 ; Vol. 31, No. 4. pp. 991-1002.

Bibtex

@article{12c4557e865447029dc6319e1b982be5,
title = "On certain classes of algebras in which centralizers are ideals",
abstract = "This paper is primarily concerned with studying finite-dimensional anti-commutative nonassociative algebras in which every centralizer is an ideal. These are shown to be anti-associative and are classified over a general field $F$; in particular, they are nilpotent of class at most $3$ and metabelian. These results are then applied to show that a Leibniz algebra over a field of charactersitic zero in which all centralizers are ideals is solvable. ",
keywords = "Anti-commutative algebra, Anti-associative algebra, Lie algebra, Leibniz algebra, mock-Lie algebra, centralizer, nilpotent algebra",
author = "David Towers and Ripan Saha",
note = "Copyright Heldermann Verlag 2021",
year = "2021",
month = nov,
day = "23",
language = "English",
volume = "31",
pages = "991--1002",
journal = "Journal of Lie Theory",
issn = "0949-5932",
publisher = "Heldermann Verlag",
number = "4",

}

RIS

TY - JOUR

T1 - On certain classes of algebras in which centralizers are ideals

AU - Towers, David

AU - Saha, Ripan

N1 - Copyright Heldermann Verlag 2021

PY - 2021/11/23

Y1 - 2021/11/23

N2 - This paper is primarily concerned with studying finite-dimensional anti-commutative nonassociative algebras in which every centralizer is an ideal. These are shown to be anti-associative and are classified over a general field $F$; in particular, they are nilpotent of class at most $3$ and metabelian. These results are then applied to show that a Leibniz algebra over a field of charactersitic zero in which all centralizers are ideals is solvable.

AB - This paper is primarily concerned with studying finite-dimensional anti-commutative nonassociative algebras in which every centralizer is an ideal. These are shown to be anti-associative and are classified over a general field $F$; in particular, they are nilpotent of class at most $3$ and metabelian. These results are then applied to show that a Leibniz algebra over a field of charactersitic zero in which all centralizers are ideals is solvable.

KW - Anti-commutative algebra

KW - Anti-associative algebra

KW - Lie algebra

KW - Leibniz algebra

KW - mock-Lie algebra

KW - centralizer

KW - nilpotent algebra

M3 - Journal article

VL - 31

SP - 991

EP - 1002

JO - Journal of Lie Theory

JF - Journal of Lie Theory

SN - 0949-5932

IS - 4

ER -