Wick-rotations of pseudo-Riemannian Lie groups

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 $\acute{E}$. Cartan's result, namely the existence and conjugacy of Cartan involutions.

To appear in J. Geom. Physics, 26 pages

References in corpus (2)

• Wick rotations and real GIT
• Real GIT with applications to compatible representations and Wick-rotations

Cited by in corpus (3)

• A construction of Einstein solvmanifolds not based on nilsolitons
• Indefinite nilsolitons and Einstein solvmanifolds
• Nice pseudo-Riemannian nilsolitons