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arXiv · 1810.12037

Wick-rotations of pseudo-Riemannian Lie groups

Christer Helleland
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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.

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Christer Helleland. 2018-10-29. Wick-rotations of pseudo-Riemannian Lie groups. https://doi.org/10.1016/j.geomphys.2020.103902

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