Abstract Several descriptions of irreducible representations of both Leavitt and hence Cohn path algebras of an arbitrary digraph with coefficients in a commutative field introduced by Chen and Rangaswamy are presented, using both infinite paths on the right and vertices as well as direct limits or factors of cyclic projective ideals of the ordinary quiver algebra. Specific properties of these irreducible representations become immediate when they are viewed as modules over the commutative subalgebras generated by symmetric idempotents of paths, thereby providing a unified way to treat them. Furthermore, their defining relations are read off, whence criteria are easily given when they are finitely presented or finite dimensional. Their endomorphism rings, and annihilator primitive ideals are also computed directly.

中文翻译：

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Leavitt 路径代数的特殊不可约表示

摘要 介绍了由 Chen 和 Rangaswamy 引入的具有交换域中系数的任意有向图的 Leavitt 和 Cohn 路径代数的不可约表示的几种描述，使用右侧和顶点上的无限路径以及循环的直接限制或因子。普通箭袋代数的射影理想。当这些不可约表示被视为由路径的对称幂等生成的交换子代数上的模块时，这些不可约表示的特定属性变得直接，从而提供了处理它们的统一方法。此外，它们的定义关系被读出，因此当它们有限地呈现或有限维时很容易给出标准。它们的自同态环和歼灭器原始理想也直接计算。