Deformations and generalized derivations of Lie conformal superalgebras

Abstract

The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Lie conformal superalgebras. Firstly, we construct the semidirect product of a Lie conformal superalgebra and its conformal module, and study derivations of this semidirect product. Secondly, we develop cohomology theory of Lie conformal superalgebras and discuss some applications to the study of deformations of Lie conformal superalgebras. Finally, we introduce generalized derivations of Lie conformal superalgebras and study their properties.Comment: 26page

Some results on $δ$-Hom-Jordan Lie conformal superalgebras

“…(2) If δ = 1 and α = id in Definition 2.1, then the δ-Hom-Jordan Lie conformal superalgebra (R, δ, α) is just the Lie conformal superalgebra in Zhao [9].…”

“…Moreover, Lie conformal superalgebras have close connections to Hamiltonian formalism in the theory of nonlinear evolution equations. Zhao, Yuan and Chen developed deformation of Lie conformal superalgebras and introduced derivations of multiplicative Lie conformal superalgebras and studied their properties in [9].…”

“…Zhao, Yuan and Chen developed the cohomology theory of Hom-Lie conformal algebras and discuss some applications to the study of deformations of regular Hom-Lie conformal algebras. Also, they introduced derivations of multiplicative Hom-Lie conformal algebras and study their properties in [10], which is different from [9]. Ma and Chen introduced the notions of δ-Hom-Jordan Lie superalgebras and discussed the concepts of α k -derivations, representations and T * -extensions of δ-Hom-Jordan Lie superalgebras in detail, and established some cohomological characterizations in [4].…”

Conformal $(\si,\t)$-Derivations on Lie conformal superalgebras

“…The derivation theory of Lie conformal (super)algebras was introduced in [2,3]. Lately, the generalized derivation theory of Lie conformal (super)algebras was developed in [4,9,10]. [8,11] studied the (α, β, γ)-derivations of Lie (super)algebras.…”

Representations and derivations of Hom-Lie conformal superalgebras

“…Lie conformal superalgebras have close connections to Hamiltonian formalism in the theory of nonlinear evolution equations. Zhao, Yuan and Chen developed deformation of Lie conformal superalgebras and introduced derivations of multiplicative Lie conformal superalgebras and study their properties in [7].…”