论文标题
Leavitt Path代数的分级不可还原表示：一种新类型和完整的分类
Graded irreducible representations of Leavitt path algebras: a new type and complete classification
论文作者
论文摘要
我们提出了一类新的Leavitt Path代数的分级不可约的表示。该类是新的，因为它的表示空间对任何现有的简单陈模块都不是同构。相应的分级简单模块填写了分级的陈型模块列表，创建了一个详尽的类：任何分级简单模块的an灭者等于分级陈型模块或该新型模块的an灭者。 我们对Leavitt路径代数的分级原始理想的表征是基础图的特性，是证明这种分类完整性的主要工具。我们还指出了[K。中的Leavitt路径代数的原始理想的表征的问题。 M. Rangaswamy，《莱维特路径代数的主要理想理论》，《任意图》，J。Elgebra375（2013），73-90]。
We present a new class of graded irreducible representations of a Leavitt path algebra. This class is new in the sense that its representation space is not isomorphic to any of the existing simple Chen modules. The corresponding graded simple modules complete the list of Chen modules which are graded, creating an exhaustive class: the annihilator of any graded simple module is equal to the annihilator of either a graded Chen module or a module of this new type. Our characterization of graded primitive ideals of a Leavitt path algebra in terms of the properties of the underlying graph is the main tool for proving the completeness of such classification. We also point out a problem with the characterization of primitive ideals of a Leavitt path algebra in [K. M. Rangaswamy, Theory of prime ideals of Leavitt path algebras over arbitrary graphs, J. Algebra 375 (2013), 73 -- 90].
