论文标题
同型在相互无偏基碱基的应用中的理论，图形上的谐波分析和不正正的滑轮
Theory of homotopes in application to mutually unbiased bases, harmonic analysis on graphs and perverse sheaves
论文作者
论文摘要
本文是对同型理论的现代结果和应用的调查。引入了关联代数中脾气暴躁的元素的概念，并证明由敏感元素构建的同位物的表示类别是适当粘合的T结构的核心。计算同型的Hochschild和全局尺寸。研究了由庞李氏杆菌型在图形的繁殖力类固醇中构建的同型。结果表明，它们是一般图的Temperley-Lieb代数的商。刺穿的圆盘和具有双点的2维球上的不良皮带被识别为合适的同型的表示。讨论了理论与SL（N，C）之间的正交分解与cartan子代理的总和与线的构型的分类，与相互无偏见的基础，与量子方案，与广义Hadamard矩阵的关系。
The paper is the survey of the modern results and applications of the theory of homotopes. The notion of a well-tempered element in an associative algebra is introduced and it is proven that the category of representations of the homotope constructed by a well-tempered element is the heart of a suitably glued t-structure. Hochschild and global dimensions of the homotopes are calculated. The homotopes constructed by generalized Lapalce operators in Poincare groupoids of graphs are studied. It is shown that they are quotients of Temperley-Lieb algebras of general graphs. The perverse sheaves on a punctured disc and on a 2 dimensional sphere with a double point are identified with representations of suitable homotopes. Relations of the theory to orthogonal decompositions of sl(n, C) into the sum of Cartan subalgebras, to classifications of configurations of lines, to mutually unbiased bases, to quantum protocols, to generalized Hadamard matrices are discussed.
