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Wick-rotations of pseudo-Riemannian Lie groups
Journal of Geometry and Physics ( IF 1.6 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.geomphys.2020.103902
Christer Helleland

Abstract 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 E . Cartan’s result, namely the existence and conjugacy of Cartan involutions.

中文翻译:

伪黎曼李群的灯芯旋转

摘要 我们使用真实 GIT 的结果(Helleland 和 Hervik,2018 年;Helleland 和 Hervik,2019 年)研究了李群上左不变度量的 Wick 旋转。给出了李群 Wick 旋转的不变量,我们描述了何时可以将伪黎曼李群(具有左不变度量的李群)Wick 旋转为黎曼李群。我们定义一般李代数的嘉当对合,并证明 E 的一般版本。嘉当的结果,即嘉当对合的存在性和共轭性。
更新日期:2020-12-01
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