Diagram groups, braid groups, and orderability

被引：4

作者：

Wiest, B ^{[1
]}

机构：

[1] Univ Rennes 1, UFR Math, F-35042 Rennes, France

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2003年 / 12卷 / 03期

关键词：

diagram group; braid group; Thompson group; orderable group;

D O I：

10.1142/S0218216503002482

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that all diagram groups (in the sense of Guba and Sapir) are left-orderable. The proof is in two steps: firstly, it is proved that all diagram groups inject in a certain braid group on infinitely many strings, and secondly, this group is then shown to be left-orderable.

引用

页码：321 / 332

页数：12

共 50 条

[1] The Representations of Braid Groups Obtained by Yang Diagram Method
仝殿民
朱诚久
Progress in Natural Science Communication of State Key Laboratories of China, 1993, (01) : 39 - 48
[2] Braid groups and symplectic Steinberg groups
Digne, Francois
Kassel, Christian
ANNALS OF K-THEORY, 2023, 8 (04) : 669 - 692
[3] Diagrammatics for Coxeter groups and their braid groups
Elias, Ben
Williamson, Geordie
QUANTUM TOPOLOGY, 2017, 8 (03) : 413 - 457
[4] Parametrized braid groups of Chevalley groups
Loday, JL
Stein, MR
DOCUMENTA MATHEMATICA, 2005, 10 : 391 - 416
[5] Affine braid groups: a better platform than braid groups for cryptology?
Ping Zhu
Qiaoyan Wen
Applicable Algebra in Engineering, Communication and Computing, 2011, 22 : 375 - 391
[6] Affine braid groups: a better platform than braid groups for cryptology?
Zhu, Ping
Wen, Qiaoyan
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2011, 22 (5-6) : 375 - 391
[7] Orders on braid groups
N. Ya. Medvedev
Algebra and Logic, 2003, 42 (3) : 177 - 180
[8] Braid groups are linear
Bigelow, SJ
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 14 (02) : 471 - 486
[9] Braid groups in cryptology
Lee, EK
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2004, E87A (05): : 986 - 992
[10] Computation of Centralizers in Braid groups and Garside groups
Franco, N
González-Meneses, J
REVISTA MATEMATICA IBEROAMERICANA, 2003, 19 (02) : 367 - 384

← 1 2 3 4 5 →