We show that a structural matrix algebra $A$ is isomorphic to the endomorphism algebra of an algebraic-combinatorial object called a generalized flag. If the flag is equipped with a group grading, an algebra grading is induced on $A$. We classify the gradings obtained in this way as the orbits of the action of a double semidirect product on a certain set. Under some conditions on the associated graph, all good gradings on $A$ are of this type. As a bi-product, we obtain a new approach to compute the automorphism group of a structural matrix algebra.

中文翻译：

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结构矩阵代数、广义标志和分级

我们证明结构矩阵代数 $A$ 与称为广义标志的代数组合对象的自同构代数同构。如果标志配备了组评分，则在 $A$ 上诱导代数评分。我们将通过这种方式获得的分级分类为双半直积在某个集合上的作用轨道。在相关图表的某些条件下，$A$ 上的所有良好评分都属于这种类型。作为副产品，我们获得了一种计算结构矩阵代数的自同构群的新方法。