IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4471-0039-3_6.html
   My bibliography  Save this book chapter

Representation theory of finite groups

In: Further Algebra and Applications

Author

Listed:
  • P. M. Cohn

    (University College London, Department of Mathematics)

Abstract

Although much of the theory of finite-dimensional algebras had its origins in the theory of group representations, it seems simpler nowadays to develop the theory of algebras first and then use it to give an account of group representations. This theory has been a powerful tool in the study of groups, especially the modular theory (representations over a field of finite characteristic), which has played a key role in the classification of finite simple groups. The theory also has important appli­cations to physics: quantum mechanics describes physical systems by means of states which are represented by vectors in Hilbert space (infinite-dimensional complete unitary space). Any group which may act on the system, such as the rotation group or a permutation group of the constituent particles, acts by unitary trans­formations on this Hilbert space and any finite-dimensional subspace admitting the group leads to a representation of the group. If we know the irreducible repre­sentations of our group, this will often allow us to classify these spaces

Suggested Citation

  • P. M. Cohn, 2003. "Representation theory of finite groups," Springer Books, in: Further Algebra and Applications, chapter 6, pages 221-264, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4471-0039-3_6
    DOI: 10.1007/978-1-4471-0039-3_6
    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:978-1-4471-0039-3_6. 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.