Restricted Cohomology of Restricted Lie Superalgebras  

作　　者：Ji Xia YUAN Liang Yun CHEN Yan CAO 

机构地区：[1]School of Mathematical Sciences,Heilongjiang University,Harbin 150080,P.R.China [2]School of Mathematical and Statistics,Northeast Normal University,Changchun 130024,P.R.China [3]Department of Mathematics,Harbin University of Science and Technology,Harbin 150080,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第11期2115-2130,共16页数学学报（英文版）

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);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)。

摘　　要：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.

关 键 词：Restricted Lie superalgebras restricted cohomology restricted model filiform Lie superalgebras 

分 类 号：O152.5[理学—数学]