»ã±¨±êÌâ (Title)£ºFrobenius-Perron theory of the bound quiver algebras containing loops £¨º¬È¦µÄÓнç¼ýͼ´úÊýµÄFrobenius-PerronÀíÂÛ£©

»ã±¨ÈË (Speaker)£º ³Â½¡Ãô ½ÌÊÚ£¨ÏÃÃÅ´óѧ£©

»ã±¨¹¦·ò (Time)£º2022Äê 5Ô 28 ÈÕ 9£º30-10£º20 (ÖÜ Áù )

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»ã±¨ÌáÒª£ºThe 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.