Strongly connected simply laced quivers and their eigenvectors
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We study the relationship between the isomorphism of quivers and properties of their spectra. It is proved that strongly connected simply laced quivers with at most four vertices are isomorphic to one another if and only if their characteristic polynomials coincide and their left and right normalized positive eigenvectors that correspond to the index can be obtained from one another by the permutation of their coordinates. An example showing that this statement is not true for quivers with five vertices is given.
KeywordsAdjacency Matrix Characteristic Polynomial Simple Root Dynkin Diagram Permutation Matrix
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