Monatshefte für Mathematik

, Volume 100, Issue 3, pp 183–210

Lorentzian cones in real Lie algebras

  • Joachim Hilgert
  • Karl H. Hofmann
Article

DOI: 10.1007/BF01299267

Cite this article as:
Hilgert, J. & Hofmann, K.H. Monatshefte für Mathematik (1985) 100: 183. doi:10.1007/BF01299267

Abstract

A Lorentzian coneW in a finite dimensional real Lie algebraL is the convex closed cone bounded by one half of the zero-set of a Lorentzian formq onL with the additional property, that for all sufficiently smallx, yW the Campbell-Hausdorff productx*y=x+y+1/2[x,y]+..., is also inW. We characterize Lorentzian cones completely; in particular, with the exception of one class of “almost abelian” solvable algebras, the Lorentzian formq is invariant, i.e., satisfiesq([x, y], z)=q (x,[y, z]).

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Joachim Hilgert
    • 1
  • Karl H. Hofmann
    • 1
  1. 1.Fachbereich MathematikTHDDarmstadtGermany