Skip to main content
SpringerLink
Log in

Spectrally ordered Lie algebras

  • I. Representations Theory of Finite and Infinite Dimensional Groups
  • Conference paper
  • First Online:
Group Theoretical Methods in Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 313))

  • 189 Accesses

Abstract

We study ordered vector spaces which are at the same time Lie algebras and satisfy certain compatibility conditions between the algebraic and the order structure. The main point is that the ordering of the Lie algebra is completely determined by the induced ordering on a Cartan algebra.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alfsen, E.M. and F.W. Shultz, Noncommutative spectral theory for affine function spaces on convex sets. Memoirs AMS172, (1976).

    Google Scholar 

  2. Hilgert, J. and K.H. Hofmann, Compactly embedded Cartan algebras an invariant cones in Lie algebras, to appear in Advances in Mathematics.

    Google Scholar 

  3. Hilgert, J., Hofmann, K.H. and J.D. Lawson, Lie theory of semigroups, Monograph, to appear.

    Google Scholar 

  4. Petrov, A., Geometric description for quantum dynamical systems, Bulg. J. Physics12, 245–249 (1985).

    Google Scholar 

  5. Petrov, A., Invariantly ordered spectral Lie algebras as abstract dynamical systems, to appear in Reports Math. Physics.

    Google Scholar 

  6. Riedel, N., Spektraltheorie in geordneten Vektorraumen, Rev. Roum. Math.28, 33–79 (1983).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Technische Hochschule Darmstadt, D-6100, Darmstadt, Germany

    J. Hilgert

Authors
  1. J. Hilgert
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Heinz-D. Doebner Jörg-D. Hennig Tchavdar D. Palev

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Hilgert, J. (1988). Spectrally ordered Lie algebras. In: Doebner, HD., Hennig, JD., Palev, T.D. (eds) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 313. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0012256

Download citation

  • DOI: https://doi.org/10.1007/BFb0012256

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50245-6

  • Online ISBN: 978-3-540-45959-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation