Suppose the ground field F is an algebraically closed field characteristic of p>2.In this paper,we investigate the restricted cohomology theory of restricted Lie superalgebras.Algebraic interpretations of low dimen...Suppose the ground field F is an algebraically closed field characteristic of p>2.In this paper,we investigate the restricted cohomology theory of restricted Lie superalgebras.Algebraic interpretations of low dimensional restricted cohomology of restricted Lie superalgebra are given.We show that there is a family of restricted model filiform Lie superalgebra Lλp,p structures parameterized by elementsλ∈Fp.We explicitly describe both the 1-dimensional ordinary and restricted cohomology superspaces of Lλp,p with coefficients in the 1-dimensional trivial module and show that these superspaces are equal.We also describe the 2-dimensional ordinary and restricted cohomology superspaces of Lλp,p with coefficients in the 1-dimensional trivial module and show that these superspaces are unequal.展开更多
基金the National Natural Science Foundation of China(Grant Nos.11601135,11771069,11801121 and 12071405)Natural Science Foundation of Heilongjiang Province of China(Grant Nos.QC2017002 and QC2018006)+1 种基金Fundamental Research Funds for the Colleges and Universities in Heilongjiang Province(Grant No.2020-KYYWF-1018)Project funded by China Postdoctoral Science Foundation(Grant No.2018M630311)。
文摘Suppose the ground field F is an algebraically closed field characteristic of p>2.In this paper,we investigate the restricted cohomology theory of restricted Lie superalgebras.Algebraic interpretations of low dimensional restricted cohomology of restricted Lie superalgebra are given.We show that there is a family of restricted model filiform Lie superalgebra Lλp,p structures parameterized by elementsλ∈Fp.We explicitly describe both the 1-dimensional ordinary and restricted cohomology superspaces of Lλp,p with coefficients in the 1-dimensional trivial module and show that these superspaces are equal.We also describe the 2-dimensional ordinary and restricted cohomology superspaces of Lλp,p with coefficients in the 1-dimensional trivial module and show that these superspaces are unequal.
