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Hom-Lie Algebras with Derivations
In this paper, we first introduce the notion of an HLieDer triple, which includes a Hom-Lie algebra and a derivation. We define a cohomology theory...
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Local and 2-Local Derivations of Locally Simple Lie Algebras
In the present paper we study local and 2-local derivations of the classical locally simple Lie algebras. Firstly, we prove that every local and...
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Local Derivations of Classical Simple Lie Algebras
The paper is devoted to study of local derivations on classical simple Lie algebras. We prove that every local derivation on an arbitrary classical...
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On \((\lambda ,\mu ,\gamma )\) -Derivations of BiHom-Lie Algebras
In this paper, we generalize the results about generalized derivations of Lie algebras to the case of BiHom-Lie algebras. In particular we give the...
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Generalized Lie Triple Derivations of Trivial Extension Algebras
In this article, we give the structure of generalized Lie triple derivations of trivial extension algebras and prove that under certain appropriate...
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Finite-Dimensional Nilpotent Lie Algebras with Central Derivations of Nonminimal Dimensions
Let L be a finite-dimensional nilpotent Lie algebra and let Der z ( L ) and C ∗ ( L ) denote the set of all central derivations and central derivations map...
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Lie Bialgebra Structure of Derivation Lie Algebra over Quantum Torus
In this paper, all Lie bialgebra structures on the derivation Lie algebra W over a rank d ≥ 3 quantum torus associated to q are considered, where q ...
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On Lie-Type Constructions over Twisted Derivations
In this paper we examine interactions between \((\sigma ,\tau )\)...
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2-Local Derivations on the Schrödinger Algebra
The present paper is devoted to study 2-local derivations on the Schrödinger algebra which is a finite-dimensional, non-semisimple and non-solvable...
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b-generalized skew derivations acting on Lie ideals in prime rings
Let R be any noncommutative prime ring of char( R ) ≠ 2, 3, L a noncentral Lie ideal of R and F, G two nonzero b -generalized skew derivations of R ....
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Characterizations of Lie derivations on Kadison–Singer algebras
Kadison–Singer algebra (KS-algebra) is a new class of non-self-adjoint operator algebras. In this paper, we mainly study the standardization of Lie...
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On Some Properties of Generalized \({\textsf{Lie}}\) -Derivations of Leibniz Algebras
We classify and deduce some properties on \(\textsf{Lie}\)...
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Automorphisms, Derivations and Gradings of the Split Quartic Cayley Algebra
The split quartic Cayley algebra is a structurable algebra which has been used to give constructions of Lie algebras of type D4. Here, we calculate...
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Commuting Iterates of Generalized Derivations on Lie Ideals
Let R be a prime ring of characteristic different from 2, \(Q_r\)...
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On \((\sigma ,\tau )\) -Derivations of Group Algebra as Category Characters
For the space of \((\sigma ,\tau )\) -derivations of the...
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Centralizers of Linear and Locally Nilpotent Derivations
Let 𝕂 be an algebraically closed field of characteristic zero, let 𝕂[ x 1 ,…, x n ] be the polynomial algebra, and let W n (𝕂) be the Lie algebra of all...