Generalized derivations, quasiderivations and centroids of Bihom-Lie triple system

In this paper, we give some properties of the generalized derivation algebra [Formula: see text] of a Bihom-Lie triple system [Formula: see text]. In particular, we prove that [Formula: see text], the sum of the quasiderivation algebra and the quasicentroid. We also prove that [Formula: see text] can be embedded as derivations in a larger Bihom-Lie triple system.

The Classification, Automorphism Group, and Derivation Algebra of the Loop Algebra Related to the Nappi–Witten Lie Algebra

Set L ≔ H 4 ⊗ ℂ R , R ≔ ℂ t ± 1 , and S ≔ ℂ t ± 1 / m m ∈ ℤ + . Then, L is called the loop Nappi–Witten Lie algebra. R -isomorphism classes of S / R forms of L are classified. The automorphism group and the derivation algebra of L are also characterized.

The Even Part of Finite-Dimensional Modular Lie Superalgebra Γ

Let [Formula: see text] be the underlying base field of characteristic [Formula: see text] and denote by [Formula: see text] the even part of the finite-dimensional Lie superalgebra [Formula: see text]. We give the generator sets of the Lie algebra [Formula: see text]. Using certain properties of the canonical tori of [Formula: see text], we describe explicitly the derivation algebra of [Formula: see text].

Derivation algebra of semi-direct sum of Lie algebras

Let [Formula: see text] and [Formula: see text] be two Lie algebras over an arbitrary field [Formula: see text], and let [Formula: see text] be the semidirect sum of [Formula: see text] by [Formula: see text]. In this paper, we give the structure of derivation algebra of [Formula: see text]; then as a consequence we illustrate the structure and dimension derivation algebra of Heisenberg Lie algebras.

Generalized conformal derivations of Lie conformal algebras

Let [Formula: see text] be a finite Lie conformal algebra. The purpose of this paper is to investigate the conformal derivation algebra [Formula: see text], the conformal quasiderivation algebra [Formula: see text] and the generalized conformal derivation algebra [Formula: see text]. The generalized conformal derivation algebra is a natural generalization of the conformal derivation algebra. Obviously, we have the following tower [Formula: see text], where [Formula: see text] is the general Lie conformal algebra. Furthermore, we mainly research the connection of these generalized conformal derivations. Finally, the conformal [Formula: see text]-derivations of Lie conformal algebras are studied. Moreover, we obtain some connections between several specific generalized conformal derivations and the conformal [Formula: see text]-derivations. In addition, all conformal [Formula: see text]-derivations of finite simple Lie conformal algebras are characterized.

Biderivations of the higher rank Witt algebra without anti-symmetric condition

The Witt algebra 𝔚d of rank d(≥ 1) is the derivation algebra of Laurent polynomial algebras in d commuting variables. In this paper, all biderivations of 𝔚d without anti-symmetric condition are determined. As an applications, commutative post-Lie algebra structures on 𝔚d are obtained. Our conclusions recover and generalize results in the related papers on low rank or anti-symmetric cases.

Double Derivations of n-Lie Superalgebras

Let 𝔤 be an n-Lie superalgebra. We study the double derivation algebra [Formula: see text] and describe the relation between [Formula: see text] and the usual derivation Lie superalgebra Der(𝔤). We show that the set [Formula: see text] of all double derivations is a subalgebra of the general linear Lie superalgebra gl(𝔤) and the inner derivation algebra ad(𝔤) is an ideal of [Formula: see text]. We also show that if 𝔤 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad(𝔤) in [Formula: see text] is trivial. Finally, we give that for every perfect n-Lie superalgebra 𝔤, the triple derivations of the derivation algebra Der(𝔤) are exactly the derivations of Der(𝔤).