Heisenberg超代数的导子代数

Derivation Algebra of Heisenberg Superalgebra

以Heisenberg超代数H的导子在基底上的表示矩阵为工具,得到了关于复数域上的有限维Heisenberg超代数H的导子代数和全形的结论:H的导子代数Der H是单完备的李超代数,而H的全形h(H)不是完备李超代数.

With matrix of the derivation of Heisenberg superalgebra H relative to the basis of H as a tool,we obtained some properties of the derivation algebra and holomorph of the finite dimensional Heisenberg superalgebra over the complex field C.The derivation algebra of H is simple complete,while the holomorph of H is not complete Liesuperalgebras.