Home > Research > Publications & Outputs > Leibniz algebras in which all centralizers of n...

Research

Associated organisational unit

Links

Text available via DOI:

Keywords

View graph of relations

Leibniz algebras in which all centralizers of nonzero elements are zero algebras

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

Published

Standard

Leibniz algebras in which all centralizers of nonzero elements are zero algebras. / Towers, David A.
In: Communications in Algebra, Vol. 53, No. 2, 01.02.2025, p. 681-686.

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

Harvard

Towers, DA 2025, 'Leibniz algebras in which all centralizers of nonzero elements are zero algebras', Communications in Algebra, vol. 53, no. 2, pp. 681-686. https://doi.org/10.1080/00927872.2024.2388282

APA

Towers, D. A. (2025). Leibniz algebras in which all centralizers of nonzero elements are zero algebras. Communications in Algebra, 53(2), 681-686. https://doi.org/10.1080/00927872.2024.2388282

Vancouver

Towers DA. Leibniz algebras in which all centralizers of nonzero elements are zero algebras. Communications in Algebra. 2025 Feb 1;53(2):681-686. Epub 2024 Aug 14. doi: 10.1080/00927872.2024.2388282

Author

Towers, David A. / Leibniz algebras in which all centralizers of nonzero elements are zero algebras. In: Communications in Algebra. 2025 ; Vol. 53, No. 2. pp. 681-686.

Bibtex

@article{f9e14a8dc5c144f98fb4d5e07e463e52,
title = "Leibniz algebras in which all centralizers of nonzero elements are zero algebras",
abstract = "This paper is concerned with generalizing the results for Lie CT-algebras to Leibniz algebras. In some cases our results give a generalization even for the case of a Lie algebra. Results on A-algebras are used to show every Leibniz CT-algebra over an algebraically closed field of characteristic different from 2,3 is solvable or is isomorphic to sl2(F). A characterization is then given for solvable Leibniz CT-algebras. It is also shown that the class of solvable Leibniz CT-algebras is factor closed.",
keywords = "A-algebra, CT-algebra, Leibniz algebra, centralizer, completely solvable, solvable",
author = "Towers, {David A.}",
year = "2025",
month = feb,
day = "1",
doi = "10.1080/00927872.2024.2388282",
language = "English",
volume = "53",
pages = "681--686",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor and Francis Ltd.",
number = "2",

}

RIS

TY - JOUR

T1 - Leibniz algebras in which all centralizers of nonzero elements are zero algebras

AU - Towers, David A.

PY - 2025/2/1

Y1 - 2025/2/1

N2 - This paper is concerned with generalizing the results for Lie CT-algebras to Leibniz algebras. In some cases our results give a generalization even for the case of a Lie algebra. Results on A-algebras are used to show every Leibniz CT-algebra over an algebraically closed field of characteristic different from 2,3 is solvable or is isomorphic to sl2(F). A characterization is then given for solvable Leibniz CT-algebras. It is also shown that the class of solvable Leibniz CT-algebras is factor closed.

AB - This paper is concerned with generalizing the results for Lie CT-algebras to Leibniz algebras. In some cases our results give a generalization even for the case of a Lie algebra. Results on A-algebras are used to show every Leibniz CT-algebra over an algebraically closed field of characteristic different from 2,3 is solvable or is isomorphic to sl2(F). A characterization is then given for solvable Leibniz CT-algebras. It is also shown that the class of solvable Leibniz CT-algebras is factor closed.

KW - A-algebra

KW - CT-algebra

KW - Leibniz algebra

KW - centralizer

KW - completely solvable

KW - solvable

U2 - 10.1080/00927872.2024.2388282

DO - 10.1080/00927872.2024.2388282

M3 - Journal article

VL - 53

SP - 681

EP - 686

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 2

ER -