IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i8p1935-d1127974.html
   My bibliography  Save this article

On the Higher Nash Blow-Up Derivation Lie Algebras of Isolated Hypersurface Singularities

Author

Listed:
  • Muhammad Asif

    (Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Punjab, Pakistan
    These authors contributed equally to this work.)

  • Ahmad N. Al-Kenani

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    These authors contributed equally to this work.)

  • Naveed Hussain

    (Department of Mathematics and Statistics, University of Agriculture, Faisalabad 38000, Punjab, Pakistan)

  • Muhammad Ahsan Binyamin

    (Department of Mathematics, GC University Faisalabad, Faisalabad 38000, Punjab, Pakistan
    These authors contributed equally to this work.)

Abstract

It is a natural question to ask whether there is any Lie algebra that completely characterize simple singularities? The higher Nash blow-up derivation Lie algebras L k l ( V ) associated to isolated hypersurface singularities defined to be the Lie algebra of derivations of the local Artinian algebra M n l ( V ) : = O l / ⟨ F , J n ⟩ , i.e., L k l ( V ) = D e r ( M n l ( V ) ) . In this paper, we construct a new conjecture for the complete characterization of simple hypersurface singularities using the Lie algebras L k l ( V ) under certain condition and prove it true for L k l ( V ) when k , l = 2 .

Suggested Citation

  • Muhammad Asif & Ahmad N. Al-Kenani & Naveed Hussain & Muhammad Ahsan Binyamin, 2023. "On the Higher Nash Blow-Up Derivation Lie Algebras of Isolated Hypersurface Singularities," Mathematics, MDPI, vol. 11(8), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1935-:d:1127974
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/8/1935/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/8/1935/
    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:11:y:2023:i:8:p:1935-:d:1127974. 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.