Geodesic
On Certain Classes of Algebras in which Centralizers are Ideals
Ripan Saha1 ; David A. Towers2
1Department of Mathematics, Raiganj University, Raiganj 733134, India
2Department of Mathematics and Statistics, Lancaster University, Lancaster, England
Journal of Lie Theory, Tome 31 (2021) no. 4, pp. 991-1002

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 17A30, 17A32, 17B30
Mots-clés : Anti-commutative algebra, anti-associative algebra, Lie algebra, Leibniz algebra, mock-Lie algebra, centralizer, nilpotent algebra

Ripan Saha  1   ; David A. Towers  2

1 Department of Mathematics, Raiganj University, Raiganj 733134, India
2 Department of Mathematics and Statistics, Lancaster University, Lancaster, England 
Ripan Saha; David A. Towers. On Certain Classes of Algebras in which Centralizers are Ideals. Journal of Lie Theory, Tome 31 (2021) no. 4, pp. 991-1002. http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a5/
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     title = {On {Certain} {Classes} of {Algebras} in which {Centralizers} are {Ideals}},
     journal = {Journal of Lie Theory},
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