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چکیده
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Abstract. In this paper we study the structure of arbitrary split involutive regular Hom-Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split involutive regular Hom-Lie color algebra L is of the form L = U ⊕ P [α]∈Π/∼ I[α] , with U a subspace of the involutive abelian subalgebra H and any I[α] , a well-described involutive ideal of L, satisfying [I[α] , I[β] ] = 0 if [α] 6= [β]. Under certain conditions, in the case of L being of maximal length, the simplicity of the algebra is characterized and it is shown that L is the direct sum of the family of its minimal involutive ideals, each one being a simple split involutive regular Hom-Lie color algebra. Finally, an example will be provided to characterise the inner structure of split involutive Hom-Lie color algebras.
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