2n+1维Heisenberg李代数自同构群的分解

The decomposition of the automorphism group of (2n+1)-dimensional Heisenberg Lie algebras

研究了2n+1维Heisenberg李代数的自同构群,选择自同构的矩阵表达形式,并充分利用分块矩阵的运算性质,得到2n+1维Heisenberg李代数自同构群的分解结构。研究发现5维与大于5维时的分解形式有稍许差异。

In this paper, we mainly studied the automorphism groups of(2n+1)-dimensional Heisenberg Lie algebras. We obtained the decomposition structure of the automorphism group of(2n+1)-dimensional Heisenberg Lie algebra by selecting the matrix expression of automorphism and making full use of the operational properties of partitioned matrix. The results show that there are some differences between the decomposition form of 5-dimension and that of more than 5-dimension.