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Abstract
In this paper, the conformal super-biderivations of two classes of Lie conformal superalgebras are studied. By proving some general results on conformal super-biderivations, we determine the conformal super-biderivations of the loop super-Virasoro Lie conformal superalgebra and Neveu–Schwarz Lie conformal superalgebra. Especially, any conformal super-biderivation of the Neveu–Schwarz Lie conformal superalgebra is inner.
Highlights
Lie conformal superalgebras, introduced by Kac in [1], encode the singular part of the operator product expansion of chiral fields in conformal field theory. e conformal super-algebras play important roles in quantum field theory, vertex algebras, integrable systems, and so on and have drawn much attention in the branches of physics and mathematics
As a generalization of conformal biderivations of Lie conformal algebras and a parallel concept of super-biderivations of Lie superalgebras, we introduce the concept of conformal super-biderivations on Lie conformal superalgebras
We hope that biderivations would contribute to the development of structure theories of Lie conformal superalgebras. is is our motivation to present this paper
Summary
Lie conformal superalgebras, introduced by Kac in [1], encode the singular part of the operator product expansion of chiral fields in conformal field theory. e conformal super-algebras play important roles in quantum field theory, vertex algebras, integrable systems, and so on and have drawn much attention in the branches of physics and mathematics. E authors in [15, 16] generalized biderivations of Lie algebras to the concept of super-biderivations of superalgebras independently. E authors in [17] studied super-biderivations on the super Galilean conform algebra. We hope that biderivations would contribute to the development of structure theories of Lie conformal superalgebras. We concentrate on the loop super-Virasoro Lie conformal superalgebra cls (see [6]), which is defined as a C[z]-module cls (⊕i∈ZC[z]Li) ⊕ (⊕i∈ZC[z]Gi) with a C[z]-basis Li, Gi|i ∈ Z and λ-brackets given by. Roughout this paper, all vector spaces are over the complex field C
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