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

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Leibniz algebras in which all centralisers of nonzero elements are zero algebras. / Towers, David.
In: Communications in Algebra, Vol. 53, No. 2, 28.02.2025, p. 681-686.

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

Harvard

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

Vancouver

Towers D. Leibniz algebras in which all centralisers of nonzero elements are zero algebras. Communications in Algebra. 2025 Feb 28;53(2):681-686. Epub 2024 Aug 14. doi: 10.1080/00927872.2024.2388282

Author

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

Bibtex

@article{11fd537707764c169621a76efbbead2c,
title = "Leibniz algebras in which all centralisers of nonzero elements are zero algebras",
abstract = "This paper is concerned with generalising the results for Lie $CT$-algebras to Leibniz algebras. In some cases our results give a generalisation 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 $sl_2(F)$. A characterisation is then given for solvable Leibniz $CT$-algebras. It is also shown that the class of solvable Leibniz $CT$-algebras is factor closed.",
author = "David Towers",
year = "2025",
month = feb,
day = "28",
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 centralisers of nonzero elements are zero algebras

AU - Towers, David

PY - 2025/2/28

Y1 - 2025/2/28

N2 - This paper is concerned with generalising the results for Lie $CT$-algebras to Leibniz algebras. In some cases our results give a generalisation 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 $sl_2(F)$. A characterisation 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 generalising the results for Lie $CT$-algebras to Leibniz algebras. In some cases our results give a generalisation 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 $sl_2(F)$. A characterisation is then given for solvable Leibniz $CT$-algebras. It is also shown that the class of solvable Leibniz $CT$-algebras is factor closed.

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 -