论文标题
用gelfand-kirillov尺寸<4到Morita等价的Leavitt路径代数分类
Classification of Leavitt Path Algebras with Gelfand-Kirillov Dimension <4 up to Morita Equivalence
论文作者
论文摘要
LEAVITT路径代数与DI（指控）图相关联，并且有一个组合程序（还原算法），使Digraph较小，同时保留了Morita类型。我们可以从多项式生长的Leavitt路径代数的模块类别中恢复完全降低的挖掘的顶点和大多数箭头。我们对系数是1何时的所有不可还原表示的明确分类，其中1个。我们通过serre子类别定义了模块类别的莫里塔不变过滤，因此我们获得了莫里塔（Morita还有更多。当Leavitt路径代数的Gelfand-Kirillov尺寸小于4时，加权的Hasse图（等效地，Digraph的完全降低）是一个完全不变的。
Leavitt path algebras are associated to di(rected )graphs and there is a combinatorial procedure (the reduction algorithm) making the digraph smaller while preserving the Morita type. We can recover the vertices and most of the arrows of the completely reduced digraph from the module category of a Leavitt path algebra of polynomial growth. We give an explicit classification of all irreducible representations of when the coefficients are a commutative ring with 1. We define a Morita invariant filtration of the module category by Serre subcategories and as a consequence we obtain a Morita invariant (the weighted Hasse diagram of the digraph) which captures the poset of the sinks and the cycles of $Γ$, the Gelfand-Kirillov dimension and more. When the Gelfand-Kirillov dimension of the Leavitt path algebra is less than 4, the weighted Hasse diagram (equivalently, the complete reduction of the digraph) is a complete Morita invariant.
