Journal of Lie Theory

no. 4
On Certain Classes of Algebras in which Centralizers are Ideals
Journal of Lie Theory, Volume 31 (2021) no. 4, pp. 991-1002
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 field F of characteristic different from 2; 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.
DOI: 10.5802/jolt.1205
Classification: 17A30, 17A32, 17B30
Keywords: Anti-commutative algebra, anti-associative algebra, Lie algebra, Leibniz algebra, mock-Lie algebra, centralizer, nilpotent algebra 
@article{JOLT_2021_31_4_a5,
     author = {R. Saha and D. A. Towers},
     title = {On {Certain} {Classes} of {Algebras} in which {Centralizers} are {Ideals}},
     journal = {Journal of Lie Theory},
     pages = {991--1002},
     year = {2021},
     volume = {31},
     number = {4},
     doi = {10.5802/jolt.1205},
     zbl = {1490.17001},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1205/}
}
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R. Saha; D. A. Towers. On Certain Classes of Algebras in which Centralizers are Ideals. Journal of Lie Theory, Volume 31 (2021) no. 4, pp. 991-1002. doi: 10.5802/jolt.1205

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