Abstract
In this paper, we’ll introduce the concept of sympathetic Lie color algebras and show that some classical properties of semi-simple Lie color algebras are still valid for sympathetic Lie color algebras. We prove that every Lie color algebras L contains a greatest sympathetic ideal M, and there exists a solvable ideal of L denoted by P(L) which is the greatest among the solvable ideals I of L for which \(I\cap M = \{ 0\}\). And we show that there exists a sympathetic subalgebra m of L such that \(L = m \oplus P(L)\) and L is a sympathetic Lie color algebra if and only if \(P(L)= \{ 0\}\). What’s more, we also study the ideals I of a Lie color algebra L such that L/I is a sympathetic Lie color algebra and get some properties about them.
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Abdaoui, M. Structure of sympathetic Lie color algebras. Rend. Circ. Mat. Palermo, II. Ser 72, 4273–4288 (2023). https://doi.org/10.1007/s12215-023-00972-7
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DOI: https://doi.org/10.1007/s12215-023-00972-7