论文标题
结合箭量代数的Frobenius-Perron理论包含循环
Frobenius-Perron theory of the bound quiver algebras containing loops
论文作者
论文摘要
基质的光谱半径，也称为Frobenius-Perron维度，是研究线性代数的有用工具，在代数的表示类别的分类中起着重要作用。在本文中，我们研究了包含循环的结合箭量代数的表示类别的Frobenius-Perron理论，找到了一种计算这些代数的Frobenius-Perron维度的方法，当它们满足环路的通勤条件。作为一个应用程序，我们证明了修改后的ADE ADE有限箭量代数的表示类别的Frobenius-Perron维度等于顶点处的最大环数。最后，我们指出的是，存在的frobenius-perron维度也等于通过举例说明的最大环数。
The spectral radius of matrix, also known as Frobenius-Perron dimension, is a useful tool for studying linear algebras and plays an important role in the classification of the representation categories of algebras. In this paper, we study the Frobenius-Perron theory of the representation categories of bound quiver algebras containing loops, find a way to calculate the Frobenius-Perron dimension of these algebras when they satisfy the commutativity condition of loops. As an application, we prove that the Frobenius-Perron dimension of the representation category of a modified ADE bounded quiver algebra is equal to the maximum number of loops at a vertex. Finally, we point out that there also exists infinite dimensional algebras whose Frobenius-Perron dimension is equal to the maximal number of loops by giving an example.
