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 maxim...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.展开更多
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).
文摘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.
