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Frobenius-Perron theory of the bound quiver algebras containing loops.

Authors :
Chen, J. M.
Chen, J. Y.
Source :
Communications in Algebra. 2024, Vol. 52 Issue 2, p845-864. 20p.
Publication Year :
2024

Abstract

The Frobenius-Perron dimension of a matrix, also known as the spectral radius, 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, and find a way to calculate the Frobenius-Perron dimensions of these algebras satisfying 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 maximal number of loops at each vertex. Finally, we point out that there also exist infinite dimensional algebras whose Frobenius-Perron dimensions is equal to the maximal number of loops by giving an example. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00927872
Volume :
52
Issue :
2
Database :
Academic Search Index
Journal :
Communications in Algebra
Publication Type :
Academic Journal
Accession number :
175363422
Full Text :
https://doi.org/10.1080/00927872.2023.2250862