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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Structural matrix algebras, generalized flags, and gradings


Authors: F. Beşleagă and S. Dăscălescu
Journal: Trans. Amer. Math. Soc. 373 (2020), 6863-6885
MSC (2010): Primary 16W50, 16W20, 16S50, 06A06
DOI: https://doi.org/10.1090/tran/8126
Published electronically: July 28, 2020
MathSciNet review: 4155194
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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 byproduct, we obtain a new approach to compute the automorphism group of a structural matrix algebra.


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Additional Information

F. Beşleagă
Affiliation: Facultatea de Matematica, University of Bucharest, Str. Academiei 14, Bucharest 1, RO-010014, Romania
Email: filoteia_besleaga@yahoo.com

S. Dăscălescu
Affiliation: Facultatea de Matematica, University of Bucharest, Str. Academiei 14, Bucharest 1, RO-010014, Romania
Email: sdascal@fmi.unibuc.ro

Keywords: Structural matrix algebra, preorder relation, flag, group grading, automorphism group.
Received by editor(s): March 27, 2017
Received by editor(s) in revised form: August 28, 2019
Published electronically: July 28, 2020
Additional Notes: This work was supported by a grant of the Ministry of Research and Innovation, CNCS - UEFISCDI, project number PN-III-P4-ID-PCE-2016-0065, within PNCDI III
Dedicated: Dedicated to Leon Van Wyk for his sixtieth birthday
Article copyright: © Copyright 2020 American Mathematical Society