Cartan型模李超代数W(n)的伴随模

Adjoint Modules of Cartan Type Modular Lie Superalgebras W(n)

Cartan型模李超代数的分类是解决素特征域上单李超代数分类问题的关键。识别定理为素特征域上李代数分类问题的解决奠定了基础。仿照识别定理中对于Cartan型模李代数伴随模的理论,研究了Cartan型模李超代数W(n)的伴随模。通过对W(n)的Z_(2)-阶化分支的直和分解,得到了两类伴随模,进而给出了这两类伴随模之间的关系,并证明了它们的不可约性。

The classification of Cartan type modular Lie superalgebras is the key of the classification of Lie superalgebras over a fields of prime characteristic.The Recognition Theorem established foundation for the classification of Lie algebras over a fields of prime characteristic.According to the theories on adjoint modules of Cartan type modular Lie algebras in Recognition Theorem,we study the adjoint modules of Cartan type modular Lie superalgebras W(n).By virtue of the direct sum decomposition of the Z_(2)-graded components in W(n),we obtain two types of adjoint module,analyse the relationship between them,and prove their irreducibilities.