李代数平凡扩张的自同构群和导子李代数

On groups of automorphisms and derivation Lie algebras of trivial extensions of Lie algebras

对于李代数g的通过模V的平凡扩张g∝V,作者分别构造了它的自同构群和导子李代数的由半直积给出的子群和子代数.作为应用,作者在单李代数及其有限维单模上得到了相应的自同构群和导子李代数的完整刻画.

For the trivial extension 9 oc V of a Lie algebra g by a g module V, the authors construct a subgroup （resp. a subalgebra） via semidirect products of the group of automorphisms of θ∝V （resp. the derivation Lie algebra）. As an application to simple Lie algebras and their finitedimensional modules, the corresponding groups of automorphisms and derivations are determined.