IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-030-45193-6_7.html

Lie Groups

In: Differentiable Manifolds

Author

Listed:
  • Gerardo F. Torres del Castillo

    (Benemérita Universidad Autónoma de Puebla, Instituto de Ciencias)

Abstract

In many applications one encounters groups of transformations which contain one or several parameters, and on these groups we can define a structure of differentiable manifold. Two examples are the isometries of a Riemannian manifold and the symmetries of a second-order ODE, considered in Sects. 6.1 and 4.3 , respectively. In this chapter we shall study these groups by themselves, combining their algebraic and differentiable structures. One of the main results of this combination is the fact that each of these groups has an associated Lie algebra which almost entirely determines the group.

Suggested Citation

  • Gerardo F. Torres del Castillo, 2020. "Lie Groups," Springer Books, in: Differentiable Manifolds, edition 2, chapter 0, pages 203-255, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-45193-6_7
    DOI: 10.1007/978-3-030-45193-6_7
    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

    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:978-3-030-45193-6_7. 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.