论文标题
有限的简单谎言伪algebras IV上的不可还原模块。非主要伪algebras
Irreducible modules over finite simple Lie pseudoalgebras IV. Non-primitive pseudoalgebras
论文作者
论文摘要
令D \子集d'为有限维度为代数，h = u（d），h'= u（d'）相应的通用包裹的代数赋予了共同交流性霍普夫代数结构。我们表明，如果L是H上的原始谎言，则所有有限的不可约L'= CUR_H^{h'} l-modules的形式为cur_h^{h'} V的形式，其中v是一种不可修复的l模型，有单个类别的例外。实际上，当L = H（D，χ，ω）时，我们引入了非当前L'模型，通过根据\ d'\ setMinus d的元素t \ in Vertrains t \ in \ d'\ setMinus d修改当前的假性，该伪动是必须满足某些技术条件的。这与[BDK1，BDK2，BDK3]的结果一起完成了有限的简单谎言模块的有限不可减至的模块，这些模块是有限二维的lie lie代数的通用包围代数上的。
Let d \subset d' be finite-dimensional Lie algebras, H = U(d), H'=U(d') the corresponding universal enveloping algebras endowed with the cocommutative Hopf algebra structure. We show that if L is a primitive Lie pseudoalgebra over H then all finite irreducible L' = Cur_H^{H'} L-modules are of the form Cur_H^{H'} V, where V is an irreducible L-module, with a single class of exceptions. Indeed, when L = H(d, χ, ω), we introduce non current L'-modules that are obtained by modifying the current pseudoaction with an extra term depending on an element t \in \d' \setminus d, which must satisfy some technical conditions. This, along with results from [BDK1, BDK2, BDK3], completes the classification of finite irreducible modules of finite simple Lie pseudoalgebras over the universal enveloping algebra of a finite-dimensional Lie algebra.
