一类n-李代数的自同构群及其导子李代数

Automorphism groups and derivation Lie algebras of a class of n-Lie algebras

对任意的n-李代数L,作者利用L的内导子李代数Inn(L)的任意模V构造了n-李代数L∝V,在此基础上利用从L到V的导子刻画了L∝V的自同构群的一个子群和导子李代数的一个子代数.对于单n-李代数L及有限维Inn(L)-模V,作者证明了从L到V的导子都是内导子.

Given an n-Lie algebra L and a module V of the Lie algebra Inn（L）, we construct an n-Lie algebra LocV, where Inn（L） is the Lie algebra of all inner derivations of L. Using derivations from L to V, we describe a subgroup of the automorphism group and a subalgebra of the derivation Lie algebra of LocV, generalizing corresponding results on Lie algebras. It is also shown that all derivations from a simple n-Lie algebra L to a finite dimensional Inn（L）-module V are inner.