Journal of Lie Theory 34 (2024), No. 2, 249--265
Copyright Heldermann Verlag 2024
Left-Symmetric Products on Cosymplectic Lie Algebras
Said El Bourkadi
Dept. of Mathematics, Faculty of Sciences, Ibn Tofail University, Kenitra, Morocco
said.elbourkadi@uit.ac.ma
Mohammed W. Mansouri
Dept. of Mathematics, Faculty of Sciences, Ibn Tofail University, Kenitra, Morocco
mansourimohammed.wadia@uit.ac.ma
We prove some properties of the cosymplectic Lie algebras and show, in particular, that they support a left-invariant product. We also provide some methods to construct these algebras and classify them in dimensions three and five. These constructions provide a large class of left-symmetric algebras in odd dimensions.
Keywords: Cosymplectic structures, left-symmetric product, double extensions.
MSC: 3D15, 22E25.
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