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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Structural matrix algebras, generalized flags, and gradings
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by F. Beşleagă and S. Dăscălescu PDF
Trans. Amer. Math. Soc. 373 (2020), 6863-6885 Request permission

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
  • 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
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 6863-6885
  • MSC (2010): Primary 16W50, 16W20, 16S50, 06A06
  • DOI: https://doi.org/10.1090/tran/8126
  • MathSciNet review: 4155194