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July 2019 Some Problems of deformations on three-step nilpotent Lie groups
Ali Baklouti, Mariem Boussoffara, Imed Kedim
Hiroshima Math. J. 49(2): 195-233 (July 2019). DOI: 10.32917/hmj/1564106545


Let $G$ be an exponential solvable Lie group and $H$ a connected Lie subgroup of $G$. Given any discontinuous group $\mathit{\Gamma}$ for the homogeneous space $\mathscr M = G/H$ and any deformation of $\mathit{\Gamma}$, deformation of discrete subgroups may destroy proper discontinuity of the action on $\mathscr M$ as $H$ is not compact (except the case when it is trivial). To interpret this phenomenon in the case when $G$ is a 3-step nilpotent, we provide a layering of Kobayashi’s deformation space $\mathscr T(\mathit{\Gamma}, G, H)$ into Hausdorff spaces, which depends upon the dimensions of $G$-adjoint orbits of the corresponding parameter space. This allows us to establish a Hausdorffness theorem for $\mathscr T(\mathit{\Gamma}, G, H)$.


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Ali Baklouti. Mariem Boussoffara. Imed Kedim. "Some Problems of deformations on three-step nilpotent Lie groups." Hiroshima Math. J. 49 (2) 195 - 233, July 2019.


Received: 27 January 2017; Revised: 2 November 2018; Published: July 2019
First available in Project Euclid: 26 July 2019

zbMATH: 07120740
MathSciNet: MR3984992
Digital Object Identifier: 10.32917/hmj/1564106545

Primary: 12A34, 98B76
Secondary: 23C57

Rights: Copyright © 2019 Hiroshima University, Mathematics Program


Vol.49 • No. 2 • July 2019
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