特殊导子李超代数的完备性

The Completeness of the Special Derivation of Lie Superalgebra

研究了李超代数的完备性问题,把完备李代数研究中的导子塔方法应用于李超代数中。通过对给定的中心平凡的李超代数,以及由它诱导的一个李超代数和诱导李超代数全形的讨论,证明了原李超代数导子代数的维数公式,进而得到了其导子李超代数的完备性。

The completeness of Lie superalgebra is studied.The derivation tower method of the completeness of Lie algebra is applied to the Lie superalgebra.The given Lie superalgebra with trivial centre,the Lie superalgebra which is induced by the given Lie superalgebra and the holomorph of the induced Lie superalgebra are discussed.The dimension formula of derivation of original Lie superalgebra is proved.And then the completeness of superderivation of Lie superalgebra is obtained.