The Structure Of The Automorphism Group Of Heisenberg Lie Algebras

Heisenberg Lie algebra is a kind of important Lie algebras.The paper mainly discusses the structure of the automorphism group of Heisenberg Algebras.Automorphism plays an important role in the structural theory of Lie algebras.In 2007,Zhang Haishan and others studied the automorphism of Heisenberg Lie algebra.The author aims at two definitions of Heisenberg Lie algebra.The necessary and sufficuent conditions for the automorphism in the first definition are discussed,and the structure of the automorphism group under the second defined forms is discussed.This paper,we study the structure of the first definition of Heisenberg Lie algebra by matrix.We obtain a necessary and sufficient condition for automorphisms of Lie algebras.The decomposition structure of automorphism groups of Lie algebras in 3 dimensional and 5 dimensional cases is obtained.