Automorphisms Of Low-dimensional Nilpotent Lie Algebras

Study of automorphisms of Lie algebras is an important aspect for its theoryresearch.Great achievements have been made in the automorphisms of semi-simple Liealgebra on the complex field, but there are few studies in automorphisms of nilpotent Liealgebra, because of the complex structure of nilpotent Lie algebras. It is an effective wayfor characterizing the automorphisms of Lie algebra to find out some equivalent conditionsof the automorphisms. The2-step nilpotent Lie algebra is an important one with simplestructure among nilpotent Lie algebra. Most of the current researches on the2-stepnilpotent Lie algebra are to do complex calculation according to the definition ofautomorphisms, so when the dimension is high, the process of calculation is complex. Thispaper adopts the matrix representation to study the automorphisms of2-step nilpotent Liealgebra whose central dimension is greater than1. By smart matrix computing, somenecessary and sufficient conditions of automorphisms of certain nilpotent Lie algebra canbe acquired, which goes with less knowledge tools and avoids the complicated calculation.This paper gives a necessary and sufficient condition for automorphisms of2-stepnilpotent Lie algebra whose central dimension is2,3, and we ascertain the automorphismgroup of certain Lie algebras and disscuss the decomposition of the specific of the Liealgebra...