Homogeneous space with non virtually abelian discontinuous groups but without any proper SL(2,R)-action
Homogeneous space with non virtually abelian discontinuous groups but without any proper SL(2,R)-action
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具有非几乎阿贝尔不连续群但没有任何适当 SL(2,R) 作用的齐次空间
DOI：
10.1142/s0129167x1650018x
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Takayuki Okuda
中科院分区：
文献类型：
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作者：
Shyuichi Izumiya;Hiroyuki Inou;Yoshitsugu Takei;Satoshi Koike;長田博文;H. Isozaki;Takayuki Okuda
在非黎曼齐性空间的不连续群的研究中，“连续类比”的思想提供了一种强有力的方法（T。小林[Math.Ann.1989]）。例如，一个半单对称空间允许一个非虚交换的不连续群当且仅当它允许一个真作用（T。Okuda [J. Differ. Geom.2013]）。然而，离散子群的作用并不总是近似于连通群的作用。本文证明了该定理不能推广到一般的还原型齐性空间。我们给出了一个反例。
In the study of discontinuous groups for non-Riemannian homogeneous spaces, the idea of “continuous analogue” gives a powerful method (T. Kobayashi [Math. Ann.1989]). For example, a semisimple symmetric spaceadmits a discontinuous group which is not virtually abelian if and only ifadmits a proper-action (T. Okuda [J. Differ. Geom.2013]). However, the action of discrete subgroups is not always approximated by that of connected groups. In this paper, we show that the theorem cannot be extended to general homogeneous spacesof reductive type. We give a counterexample in the case.