一类Contact型李超代数的超导子代数

Superderivation algebras for a family of Lie superalgebras of contact type

研究特征p>3的域上的外代数与有限维Contact型李代数的张量积所构成的李超代数的结构。通过计算确定这类李超代数的乘法生成元,进而获得它们的超导子代数。此类Contact型李超代数的超导子均来自外代数的导子代数,以及以除幂代数为底代数的Contact型李代数的外导子。

The structure of the Lie superalgebra （ that is, the tensor product of the exterior algebra and the finite-di- mensional generalized Contact-type Lie algebra over a field of characteristic p 〉 3 ） is considered. By means of com- putation, the generators are first given and then the superderivation algebra is determined. Superderivation of the Lie superalgebra of Contact-type consists of derivation of exterior algebra and derivation of Contact-type Lie algebra for which its underlying algebra is divided power algebra.