IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-540-85332-9_2.html
   My bibliography  Save this book chapter

Weakly Nonassociative Algebras, Riccati and KP Hierarchies

In: Generalized Lie Theory in Mathematics, Physics and Beyond

Author

Listed:
  • Aristophanes Dimakis

    (University of the Aegean, Department of Financial and Management Engineering)

  • Folkert Müller-Hoissen

    (Max-Planck-Institute for Dynamics and Self-Organization, Bunsenstrasse 10)

Abstract

It has recently been observed that certain nonassociative algebras (called ‘weakly nonassociative‐, WNA) determine, via a universal hierarchy of ordinary differential equations, solutions of the KP hierarchy with dependent variable in an associative subalgebra (the middle nucleus). We recall central results and consider a class of WNA algebras for which the hierarchy of ODEs reduces to a matrix Ric-cati hierarchy, which can be easily solved. The resulting solutions of a matrix KP hierarchy determine, under a ‘rank one condition’, solutions of the scalar KP hierarchy. We extend these results to the discrete KP hierarchy. Moreover, we build a bridge from the WNA framework to the Gelfand—Dickey—Sato formulation of the KP hierarchy.

Suggested Citation

  • Aristophanes Dimakis & Folkert Müller-Hoissen, 2009. "Weakly Nonassociative Algebras, Riccati and KP Hierarchies," Springer Books, in: Sergei Silvestrov & Eugen Paal & Viktor Abramov & Alexander Stolin (ed.), Generalized Lie Theory in Mathematics, Physics and Beyond, chapter 2, pages 9-27, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-85332-9_2
    DOI: 10.1007/978-3-540-85332-9_2
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:sprchp:978-3-540-85332-9_2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.