J. Patera, P. Winternitz and H. Zassenhaus, “Continuous Subgroups of the Fundamental Groups of Physics. I. General Method and the Poincaré Group,” Journal of Mathematical Physics, Vol. 16, No. 8, 1975, pp. 1597-1614.

has been cited by the following article:

• TITLE: Nonabelian Dualization of Plane Wave Backgrounds

  AUTHORS: Ladislav Hlavatý, Miroslav Turek

  KEYWORDS: Sigma Model; String Duality; pp-Wave Background

  JOURNAL NAME: Journal of Modern Physics, Vol.3 No.9, September 25, 2012

  ABSTRACT: We investigate plane-parallel wave metrics from the point of view of their (Poisson-Lie) T-dualizability. For that purpose we reconstruct the metrics as backgrounds of nonlinear sigma models on Lie groups. For construction of dual backgrounds we use Drinfel’d doubles obtained from the isometry groups of the metrics. We find dilaton fields that enable to satisfy the vanishing beta equations for the duals of the homogenous plane-parallel wave metric. Torsion potentials or B-fields, invariant w.r.t. the isometry group of Lobachevski plane waves are obtained by the Drinfel’d double construction. We show that a certain kind of plurality, different from the (atomic) Poisson-Lie T-plurality, may exist in case that metrics admit several isometry subgroups having the dimension of the Riemannian manifold. An example of that are two different backgrounds dual to the homogenous plane-parallel wave metric.