论文标题
正面乘法图和代数的基础知识
Basics on positively multiplicative graphs and algebras
论文作者
论文摘要
当其邻接矩阵$ a $嵌入矩阵代数嵌入基础$ \ m m i \ mathsf {b} $带有非负结构常数的基础上时，呈正力的乘法呈阳性倍增。本文的目的是介绍该概念的基本属性，并通过各种简单的示例来解释其与高度非微不足道的问题的关系，例如融合规则的组合描述，分级图的最小边界的描述或在Alcove Tilings上进行随机步行的研究。
An oriented graph is said positively multiplicative when its adjacency matrix $A$ embeds in a matrix algebra admitting a basis $\mathsf{B}$ with nonnegative structure constants in which the matrix of the multiplication by $A$ coincides with $A$. The goal of this paper is to present basic properties of this notion and explain, through various simple examples, how it relates to highly non trivial problems like the combinatorial description of fusion rules, the description of the minimal boundary of graded graphs or the study of random walks on alcove tilings.
