Thompson's group F and the linear group GL a (a"currency sign)

被引：0

作者：

Wu, Yan ^{[1
]}

Chen, Xiaoman ^{[2
]}

机构：

[1] Jiaxing Univ, Coll Math Phys & Informat Engn, Jiaxing 314033, Zhejiang, Peoples R China

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2011年 / 32卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Finite decomposition complexity; Thompson's group F; Word-metric; Lipschitz map; Reduced tree diagram;

D O I：

10.1007/s11401-011-0679-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The authors study the finite decomposition complexity of metric spaces of H, equipped with different metrics, where H is a subgroup of the linear group GL(a)(a"currency sign). It is proved that there is an injective Lipschitz map phi: (F, d (S) ) -> (H, d), where F is the Thompson's group, dS the word-metric of F with respect to the finite generating set S and d a metric of H. But it is not a proper map. Meanwhile, it is proved that phi: (F, d (S) ) -> (H, d (1)) is not a Lipschitz map, where d (1) is another metric of H.

引用

页码：863 / 884

页数：22

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