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
In [21], generalized restricted Lie algebras, defined over a field F of positive characteristic p, were introduced. In this note their cohomology, especially the so-called generalized restricted cohomology is studies....In [21], generalized restricted Lie algebras, defined over a field F of positive characteristic p, were introduced. In this note their cohomology, especially the so-called generalized restricted cohomology is studies. Some reduction properties are obtained. For graded Cartan type Lie algebras the author determines the first Lie-cohomology groups and the first generalized restricted cohomology groups with the coefficients in the highest weight modules from which all irreducible generalized restricted modules are derived.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.
文摘In [21], generalized restricted Lie algebras, defined over a field F of positive characteristic p, were introduced. In this note their cohomology, especially the so-called generalized restricted cohomology is studies. Some reduction properties are obtained. For graded Cartan type Lie algebras the author determines the first Lie-cohomology groups and the first generalized restricted cohomology groups with the coefficients in the highest weight modules from which all irreducible generalized restricted modules are derived.
