单项代数的熵与导出范畴
环与代数
2023-08-29 v2 动力系统
K理论与同调
摘要
设 A 为有限呈现结合单项代数。我们研究范畴 qgr(A)，它是分次有限呈现 A-模范畴模去有限维模所得的商范畴。由于该范畴对应于相应非交换簇上的凝聚层范畴，我们考虑其有界导出范畴。我们计算了该导出范畴上 Serre 扭曲函子的范畴熵，并证明其等于代数 A 自身熵的对数。此外，我们将这两类熵与 A 的 Ufnarovski 图拓扑熵及该图路代数熵相关联。若 A 为某 quiver 的路代数，则范畴熵等于该 quiver 邻接矩阵谱半径的对数。
引用
@article{arxiv.2103.03946,
title = {Entropy of monomial algebras and derived categories},
author = {Li Lu and Dmitri Piontkovski},
journal= {arXiv preprint arXiv:2103.03946},
year = {2023}
}
备注
16 pages. In comparison to the version published in IMRN, here a paragraph is added in the beginning of the proof of Theorem 6.5 to fill a gap. In fact, in the previous version the argument was valid for quivers without sinks only