IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i2p191-d1314347.html
   My bibliography  Save this article

Tilting Quivers for Hereditary Algebras

Author

Listed:
  • Shen Li

    (School of Science, Shandong Jianzhu University, Jinan 250101, China)

Abstract

Let A be a finite dimensional hereditary algebra over an algebraically closed field k . In this paper, we study the tilting quiver of A from the viewpoint of τ -tilting theory. First, we prove that there exists an isomorphism between the support τ -tilting quiver Q (s τ -tilt A ) of A and the tilting quiver Q (tilt A ¯ ) of the duplicated algebra A ¯ . Then, we give a new method to calculate the number of arrows in the tilting quiver Q (tilt A ) when A is representation-finite. Finally, we study the conjecture given by Happel and Unger, which claims that each connected component of Q (tilt A ) contains only finitely many non-saturated vertices. We provide an example to show that this conjecture does not hold for some algebras whose quivers are wild with at least four vertices.

Suggested Citation

  • Shen Li, 2024. "Tilting Quivers for Hereditary Algebras," Mathematics, MDPI, vol. 12(2), pages 1-9, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:191-:d:1314347
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/2/191/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/2/191/
    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:12:y:2024:i:2:p:191-:d:1314347. 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.