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arXiv · 1802.03427

Structural matrix algebras, generalized flags and gradings

Filoteia Besleaga·Sorin Dascalescu
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Abstract

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.

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Filoteia Besleaga, Sorin Dascalescu. 2018-02-09. Structural matrix algebras, generalized flags and gradings. https://arxiv.org/abs/1802.03427

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