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Article

Xu, Xiaoning ; Chen, Liangyun
Some properties of the family $\Gamma $ of modular Lie superalgebras. (English). Czechoslovak Mathematical Journal, vol. 63 (2013), issue 4, pp. 1087-1112
MSC: 17B50 | MR 3165516 | Zbl 1299.17017 | DOI: 10.1007/s10587-013-0073-6
Keywords:
modular Lie superalgebra; restricted Lie superalgebra; filtration
Summary:
In this paper, we continue to investigate some properties of the family $\Gamma $ of finite-dimensional simple modular Lie superalgebras which were constructed by X. N. Xu, Y. Z. Zhang, L. Y. Chen (2010). For each algebra in the family, a filtration is defined and proved to be invariant under the automorphism group. Then an intrinsic property is proved by the invariance of the filtration; that is, the integer parameters in the definition of Lie superalgebras $\Gamma $ are intrinsic. Thereby, we classify these Lie superalgebras in the sense of isomorphism. Finally, we study the associative forms and Killing forms of these Lie superalgebras and determine which superalgebras in the family are restrictable.
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