Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 2
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    BARNES, DONALD W. 2014. CHARACTER CLUSTERS FOR LIE ALGEBRA MODULES OVER A FIELD OF NONZERO CHARACTERISTIC. Bulletin of the Australian Mathematical Society, Vol. 89, Issue. 02, p. 234.


    Barnes, Donald W. 2013. On 𝔉-Hypercentral and 𝔉-Hypereccentric Modules for Finite Soluble Groups. Communications in Algebra, Vol. 41, Issue. 5, p. 1872.


    Γ—
  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society, Volume 78, Issue 3
  • June 2005, pp. 407-421

Ado-Iwasawa extras

  • Donald W. Barnes (a1)
  • DOI: http://dx.doi.org/10.1017/S1446788700008600
  • Published online: 01 April 2009
Abstract
Abstract

Let L be a finite-dimensional Lie algebra over the field F. The Ado-Iwasawa Theorem asserts the existence of a finite-dimensional L-module which gives a faithful representation ρ of L. Let S be a subnormal subalgebra of L, let be a saturated formation of soluble Lie algebras and suppose that S ∈ . I show that there exists a module V with the extra property that it is -hypercentral as S-module. Further, there exists a module V which has this extra property simultaneously for every such S and , along with the Hochschild extra that ρ(x) is nilpotent for every x ∈ L with ad(x) nilpotent. In particular, if L is supersoluble, then it has a faithful representation by upper triangular matrices.

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the β€˜name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. β€˜@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. β€˜@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Ado-Iwasawa extras
      Your Kindle email address
      Available formats
      Γ—
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Ado-Iwasawa extras
      Available formats
      Γ—
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Ado-Iwasawa extras
      Available formats
      Γ—
Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]D. W. Barnes , β€˜On -hypercentral modules for Lie algebras’, Arch. Math. 30 (1978), 1–7.

[2]D. W. Barnes , β€˜Saturated formations of soluble Lie algebras in characteristic 0’, Arch. Math. 30 (1978), 477–480.

[5]D. W. Barnes and H. M. Gastineau-Hills , β€˜On the theory of soluble Lie algebras’, Math. Z. 106 (1968), 343–354.

[6]Harish-Chandra, β€˜Faithful representations of Lie algebras’, Ann. of Math. (2) 50 (1949), 68–76.

[7]G. Hochschild , β€˜An addition to Ado's Theorem’, Proc. Amer. Math. Soc. 17 (1966), 531–533.

[10]E. Schenkman , β€˜A theory of subinvariant Lie algebras’, Amer. J. Math. 73 (1951), 453–474.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
Γ—
MathJax

Keywords: