IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i5p455-d504758.html
   My bibliography  Save this article

Three Representation Types for Systems of Forms and Linear Maps

Author

Listed:
  • Abdullah Alazemi

    (Department of Mathematics, Kuwait University, Safat 13060, Kuwait)

  • Milica Anđelić

    (Department of Mathematics, Kuwait University, Safat 13060, Kuwait)

  • Carlos M. da Fonseca

    (Department of Mathematics, Kuwait College of Science and Technology, Safat 13133, Kuwait
    Chair of Computational Mathematics, University of Deusto, 48007 Bilbao, Spain)

  • Vyacheslav Futorny

    (Department of Mathematics, University of São Paulo, São Paulo 05508, Brazil)

  • Vladimir V. Sergeichuk

    (Institute of Mathematics, Tereshchenkivska 3, 01024 Kiev, Ukraine)

Abstract

We consider systems of bilinear forms and linear maps as representations of a graph with undirected and directed edges. Its vertices represent vector spaces; its undirected and directed edges represent bilinear forms and linear maps, respectively. We prove that if the problem of classifying representations of a graph has not been solved, then it is equivalent to the problem of classifying representations of pairs of linear maps or pairs consisting of a bilinear form and a linear map. Thus, there are only two essentially different unsolved classification problems for systems of forms and linear maps.

Suggested Citation

  • Abdullah Alazemi & Milica Anđelić & Carlos M. da Fonseca & Vyacheslav Futorny & Vladimir V. Sergeichuk, 2021. "Three Representation Types for Systems of Forms and Linear Maps," Mathematics, MDPI, vol. 9(5), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:455-:d:504758
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/5/455/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/5/455/
    Download Restriction: no
    ---><---

    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:9:y:2021:i:5:p:455-:d:504758. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.