布尔矩阵代数、对应函子和简单性

Pub Date : 2019-02-13 DOI:10.4171/jca/44

S. Bouc, Jacques Th'evenaz

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引用次数: 11

摘要

我们确定了有限集（即布尔矩阵）上所有关系的monoid代数的每个简单模的维数。事实上，这与确定一个简单对应函子的每个求值的维数是相同的问题。该方法使用了[BT2，BT3]中发展的此类函子的理论，以及有限格理论中的一些新成分。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The algebra of Boolean matrices, correspondence functors, and simplicity

We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a simple correspondence functor. The method uses the theory of such functors developed in [BT2, BT3], as well as some new ingredients in the theory of finite lattices.

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