IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i5p729-d758420.html
   My bibliography  Save this article

Wargaming with Quadratic Forms and Brauer Configuration Algebras

Author

Listed:
  • Agustín Moreno Cañadas

    (Departamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No 45-03, Bogotá 11001000, Colombia
    These authors contributed equally to this work.)

  • Pedro Fernando Fernández Espinosa

    (Departamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No 45-03, Bogotá 11001000, Colombia
    These authors contributed equally to this work.)

  • Gabriel Bravo Rios

    (Departamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No 45-03, Bogotá 11001000, Colombia
    These authors contributed equally to this work.)

Abstract

Recently, Postnikov introduced Bert Kostant’s game to build the maximal positive root associated with the quadratic form of a simple graph. This result, and some other games based on Cartan matrices, give a new version of Gabriel’s theorem regarding algebras classification. In this paper, as a variation of Bert Kostant’s game, we introduce a wargame based on a missile defense system (MDS). In this case, missile trajectories are interpreted as suitable paths of a quiver (directed graph). The MDS protects a region of the Euclidean plane by firing missiles from a ground-based interceptor (GBI) located at the point ( 0 , 0 ) . In this case, a missile success interception occurs if a suitable positive number associated with the launches of the enemy army can be written as a mixed sum of triangular and square numbers.

Suggested Citation

  • Agustín Moreno Cañadas & Pedro Fernando Fernández Espinosa & Gabriel Bravo Rios, 2022. "Wargaming with Quadratic Forms and Brauer Configuration Algebras," Mathematics, MDPI, vol. 10(5), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:729-:d:758420
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/5/729/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/5/729/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Stéphane Goria, 2011. "Information display from board wargame for marketing strategy identification," Post-Print hal-00584200, HAL.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:729-:d:758420. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.