论文标题
与Morita等效$ C^\ AST $ -Algebras的Digraphs的光谱
The spectra of digraphs with Morita equivalent $C^\ast$-algebras
论文作者
论文摘要
Eilers等。最近，使用相应的挖掘图上的一组动作完成了Unital Graph $ c^\ ast $ algebras的几何分类。我们探讨了这些动作是否保留有限挖掘谱的非零元素的问题，本文在本文中可以具有循环和平行边缘。我们考虑了文献中研究过的几种不同的挖掘光谱，回答了这个问题的拉普拉斯和邻接光谱，它们的偏斜谱，对称的邻接频谱，线digraph的邻接频谱，hermitian邻接光谱的邻接光谱，以及在大多数情况下都可以考虑到这些频谱的依次，这些谱是这些频谱的依次，这些频谱可以在这些方面存在这些频谱。我们表明，挖掘和线路挖掘的邻接光谱由移动的子集保留，并且偏斜的邻接和拉普拉斯光谱由Cuntz Splice保留。我们给出反例，以表明其余的动作并不能保留其他光谱。如果一个人限制了牢固连接的Digraphs类别，则相同的结果。
Eilers et al. have recently completed the geometric classification of unital graph $C^\ast$-algebras up to Morita equivalence using a set of moves on the corresponding digraphs. We explore the question of whether these moves preserve the nonzero elements of the spectrum of a finite digraph, which in this paper is allowed to have loops and parallel edges. We consider several different digraph spectra that have been studied in the literature, answering this question for the Laplace and adjacency spectra, their skew counterparts, the symmetric adjacency spectrum, the adjacency spectrum of the line digraph, the Hermitian adjacency spectrum, and the normalized Laplacian, considering in most cases two ways that these spectra can be defined in the presence of parallel edges. We show that the adjacency spectra of the digraph and line digraph are preserved by a subset of the moves, and the skew adjacency and Laplace spectra are preserved by the Cuntz splice. We give counterexamples to show that the other spectra are not preserved by the remaining moves. The same results hold if one restricts to the class of strongly connected digraphs.
