English

Wick-rotations of pseudo-Riemannian Lie groups

Differential Geometry 2020-09-08 v2

Abstract

We study Wick-rotations of left-invariant metrics on Lie groups, using results from real GIT (\cite{1}, \cite{2}, \cite{3}). An invariant for Wick-rotation of Lie groups is given, and we describe when a pseudo-Riemannian Lie group can be Wick-rotated to a Riemannian Lie group. We also prove a general version (for general Lie algebras) of Eˊ\acute{E}. Cartan's result, namely the existence and conjugacy of Cartan involutions.

Keywords

Cite

@article{arxiv.1810.12037,
  title  = {Wick-rotations of pseudo-Riemannian Lie groups},
  author = {Christer Helleland},
  journal= {arXiv preprint arXiv:1810.12037},
  year   = {2020}
}

Comments

To appear in J. Geom. Physics, 26 pages