The Multiplier and Cohomology of Lie Superalgebras  

作　　者：Yang Liu Wende Liu 

机构地区：[1]Department of Mathematics,Harbin Institute of Technology,Harbin 150001,China [2]School of Mathematics and Statistics,Hainan Normal University,Haikou 571158,China

出　　处：《Algebra Colloquium》2023年第3期371-384,共14页代数集刊（英文版）

基　　金：The first author(Y.Liu)was supported by the NSF of Heilongjiang Province of China(YQ2020A005);The second author(W.D.Liu)was supported by the NSF of China(12061029);the NSF of Hainan Province of China(120RC587).

摘　　要：Suppose that L is a Lie superalgebra over a field F of characteristic different from 2 and 3.In this paper,the so-called 5-sequence of cohomology for a central extension of L is constructed and is proved to be exact.Moreover,the multiplier of L is proved to be isomorphic to the second cohomology group with coefficients in the trivial module of L.Finally,an upper bound of the superdimension of the second cohomology group is given in the situation when L is nilpotent and finite-dimensional.

关 键 词：MULTIPLIER COHOMOLOGY 5-sequence 

分 类 号：O15[理学—数学]