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. This talk focuses on the Frobenius-Perron theory of the representation categories of bound quiver algebras containing loops. We 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. Moreover, 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. This is a joint work with Jiayi Chen.

会议密码:2022