【作者】 姚裕丰；

【导师】 舒斌；

【作者基本信息】 华东师范大学 ， 基础数学， 2007， 硕士

【摘要】 本文将Skryabin为了研究广义Witt代数的表示而提出来的（?）-模范畴理论建立在Cartan型李代数系列的特殊型李代数S（m；n）上。证明了广义限制李代数意义下的诱导模成为（?）-模范畴对象。从而决定了这类李代数所有广义p-特征高度不超过min{p^n_i-p^n_i-1|1≤i≤m}-2的不可约模：其中在非例外权情形不可约模即为诱导模，例外权情形不可约模为诱导模的唯一商模。对于后者，通过诱导模的Koszul复形具体构造了出来，并由此确定了高度为0的所有不可约模的同构类个数，确定了所有例外权的不可约模的维数。更多还原

【Abstract】 In this paper, we consider the (?)-module category theory in graded Cartan type special algebra S(m; n) which was firstly introduced by Skryabin to study representations of the generalized witt algebra. We prove that as a generalized restricted Lie algebra, the induced modules of S(m;n) are objects of the (?)-module category. Irreducible modules with generalized p-character no more than min are determined. In the nonexceptional case, all irreducible modules are induced modules. In the exceptional case, irrducible modules are the unique quotient modules of induced modules. For the latter case, irreducible modules are concretely constructed through the Koszul complex of induced modules. Furthermore, all isomorphism classes of irreducible modules are determined when the height of the character is 0, and the dimensions of all exceptional irreducible modules are given.更多还原