Consider a Lie color algebra, denoted by L. Our aim in this paper is to study the Lie triple derivations TDer(L) and generalized Lie triple derivations GTDer(L) of Lie color algebras. We discuss the centroids, quasi centroids and central triple derivations of Lie color algebras, where we show the relationship of triple centroids, triple quasi centroids and central triple derivation with Lie triple derivations and generalized Lie triple derivations of Lie color algebras L. A classification of Lie triple derivations algebra of all perfect Lie color algebras is given, where we prove that for a perfect and centerless Lie color algebra, TDer(L)=Der(L) and TDer(Der(L))=Inn(Der(L)).
In this paper, our objective is to study numerous fundamental properties of the algebra of generalized derivations on a multiplicative BiHom-Poisson superalgebra [Formula: see text]. First, we present a description of some generalized derivations, central derivations, quasiderivations, centroid and quasicentroid of the multiplicative BiHom-Poisson superalgebra [Formula: see text] More specifically, we obtain some important connections and properties of these derivations. We prove that in a larger multiplicative BiHom-Poisson superalgebra, [Formula: see text] can be embedded as a derivations algebra. Finally, we show that when [Formula: see text] is centerless, the derivations of the larger multiplicative BiHom-Poisson superalgebras have direct sum decompositions.
Consider a Hom–Lie superalgebra, denoted by [Formula: see text]. In this paper, we inquire the Lie triple derivation [Formula: see text] and generalized Lie triple derivation [Formula: see text] of Hom–Lie superalgebra. Later, we address the triple centroid, triple quasi-centroid and central triple derivations of Hom–Lie superalgebra. Moreover, we attempt to show the relationship of triple centroid, triple quasi-centroid and central triple derivation with [Formula: see text] and [Formula: see text]. We give complete classification of triple derivations of Hom–Lie superalgebra, where we show that for the simple Hom–Lie superalgebras [Formula: see text].
Hom-associative conformal algebra [Formula: see text] is an associative conformal algebra with a twist map and satisfies the Hom-associative conformal identity. This study aims to introduce the notion of the Rota–Baxter operator [Formula: see text] on Hom-associative conformal algebra [Formula: see text]. We generalize our study to Hom-dendriform and Hom-tridendriform conformal algebras and give their relation to Hom-preLie conformal algebras. We give the interrelation between dendriform (and tridendriform) algebra with Hom-associative conformal Rota–Baxter algebra. Furthermore, we explore the Nijenhus operator on Hom-associative conformal algebra and describe its relation with Hom-associative Rota–Baxter operator.
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