模李超代数W(m,n,t)的结构和性质

The constructions and properties of modular Lie superalgebra W(m,n,t)

讨论了素域F(charF>2)上的Cartan型模李超代数W(m,n,t)作为W(m,t)的模的结构及其子模的一些性质.通过对W(m,n,t)的分解得到其W(m,t)子模的直和分解.这些子模中一些是同构W(m,t)的不可约模,其他的是相互之间同构的不可分解模.最后依据W(m,t)对其环面子代数的根空间分解,计算了W(m,n,t)的特征标公式.

In this article,we consider the constructions of the modular Lie superalgebra W（m,n,t） over a prime field F as a module of one of its subalgebras W（m,t） and some properties of its submodules by means of the adjoint action of W（m,t） on W（m,n,t）.W（m,n,t） is a direct sum of its W（m,t）-submodules,of which some are irreducible modules that are all isomorphic to W（m,t）,while the others are indecomposable modules between any two of which there is a unique isomorphism.In the last section,the character formula of W（m,n,t） is formulated by considering the vector space decomposition of W（m,t） over a torus.