Hom-李超代数的结构

摘要

类比于单李超代数的结构性质，证明了单 Hom-李超代数没有任何非平凡的左(右)理想、理想。通过给出保积 Hom-李超代数的若干性质，建立了保积 Hom-李超代数与李超代数之间的关系。特别地，证明了正则Hom-李超代数是可解(幂零)的充要条件是其容许李超代数是可解(幂零)的，并给出了正则Hom-李超代数是单的必要条件为其容许李超代数是单的。%This paper considers finite-dimensional Hom-Lie superalgebras over a field of characteristic zero. Analogous to the structural properties of the simple Lie superalgebra, we prove that a simple Hom-Lie superal-gebra dose not have any non-trivial left or right ideals (graded or not). We establish the relationship between the multiplicative Hom-Lie superalgebra and the Lie superalgebra by giving some properties of the multiplicative Hom-Lie superalgebra. Especially, we characterize that a regular Hom-Lie superalgebra is solvable (or nilpo-tent) if and only if its admissible Lie superalgebra is solvable (or nilpotent). Furthermore, a regular Hom-Lie superalgebra is simple if its admissible Lie superalgebra is simple.