$n$-Lie conformal algebras and its associated infinite-dimensional $n$-Lie algebras

Abstract

In this paper, we introduce a {λ1→n−1}-bracket and a distribution notion of an n-Lie conformal algebra. For any n-Lie conformal algebra R, there exists a series of associated infinite-dimensional linearly compact n-Lie algebras {(L iep R) } (p≥1) . We show that torsionless finite n-Lie conformal algebras R and S are isomorphic if and only if (L iep R) ≃ (L iep S) as linearly compact n-Lie algebras with ∂t i -action for any p ≥ 1. Moreover, the representation and cohomology theory of n-Lie conformal algebras are established. In particular, the complex of R is isomorphic to a subcomplex of n-Lie algebra (L iep R) .