Multipliers,covers,and stem extensions for Lie superalgebras  

作　　者：Wende LIU Xingxue MIAO 

机构地区：[1]School of Mathematics and Statistics,Hainan Normal University,Haikou 571158,China [2]School of Mathematical Sciences,Harbin Normal University,Harbin 150025,China

出　　处：《Frontiers of Mathematics in China》2021年第4期979-995,共17页中国高等学校学术文摘·数学（英文）

基　　金：the National Natural Science Foundation of China(Grant No.12061029);the Natural Science Foundation of Hainan Province(No.120RC587);the Natural Science Foundation of Heilongjiang Province(No.YQ2020A005).

摘　　要：Suppose that the underlying field is of characteristic different from 2 and 3.We first prove that the so-called stem deformations of a free presentation of a finite-dimensional Lie superalgebra L exhaust all the maximal stem extensions of L,up to equivalence of extensions.Then we prove that multipliers and covers always exist for a Lie superalgebra and they are unique up to superalgebra isomorphisms.Finally,we describe the multipliers,covers,and maximal stem extensions of Heisenberg superalgebras and model filiform Lie superalgebras.

关 键 词：Multiplier cover stem extension Heisenberg superalgebra filiform Lie supleralgebra 

分 类 号：O17[理学—数学]