Wick-rotations of pseudo-Riemannian Lie groups
Peer reviewed, Journal article
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Date
2020Metadata
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Original version
Helleland, C. (2020) Wick-rotations of pseudo-Riemannian Lie groups. Journal of Geometry and Physics 158 . 10.1016/j.geomphys.2020.103902Abstract
We study Wick-rotations of left-invariant metrics on Lie groups, using results from real GIT (Helleland and Hervik, 2018; Helleland and Hervik, 2019). An invariant for Wick-rotation of Lie groups is given, and we describe when a pseudo-Riemannian Lie group (a Lie group with a left-invariant metric) can be Wick-rotated to a Riemannian Lie group. We define a Cartan involution of a general Lie algebra, and prove a general version of É. Cartan’s result, namely the existence and conjugacy of Cartan involutions.
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© 2020 The Author(s).