Braid groups and symplectic Steinberg groups

被引：0

作者：

Digne, Francois ^{[1
]}

Kassel, Christian ^{[2
]}

机构：

[1] Univ Picardie Jules Verne, CNRS, Lab Amienois Math Fondamentale & Appliquee, Amiens, France

[2] Univ Strasbourg, Inst Rech Math Avancee, CNRS, Strasbourg, France

来源：

ANNALS OF K-THEORY | 2023年 / 8卷 / 04期

关键词：

braid group; Artin group; Steinberg group; symplectic modular group; group presentation; CHEVALLEY GROUPS; THEOREM;

D O I：

10.2140/akt.2023.8.669

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a homomorphism f from the braid group B2n+2 on 2n + 2 strands to the Steinberg group St(Cn, 71) associated with the Lie type Cn and with integer coefficients. This homomorphism lifts the well-known symplectic representation (aka the integral Burau representation) of the braid group. We also describe the image and the kernel of f .

引用

页码：669 / 692

页数：25

共 50 条

[1] Another presentation for symplectic Steinberg groups
Lavrenov, Andrei
JOURNAL OF PURE AND APPLIED ALGEBRA, 2015, 219 (09) : 3755 - 3780
[2] Restricting the Steinberg character in finite symplectic groups
An, JB
Hiss, G
JOURNAL OF GROUP THEORY, 2006, 9 (02) : 251 - 264
[3] BRAID GROUPS AND WORD PROBLEMS IN BRAID GROUPS
LADEGAILLERIE, Y
BULLETIN DES SCIENCES MATHEMATIQUES, 1976, 100 (03): : 255 - 267
[4] Steinberg groups of orthogonal groups
Boge, S
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1998, 494 : 219 - 236
[5] Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups (with an appendix written jointly with Francois Dahmani)
Fel'shtyn, Alexander
Goncalves, Daciberg L.
GEOMETRIAE DEDICATA, 2010, 146 (01) : 211 - 223
[6] Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups (with an appendix written jointly with Francois Dahmani)
Alexander Fel’shtyn
Daciberg L. Gonçalves
Geometriae Dedicata, 2010, 146 : 211 - 223
[7] Quantum groups and braid groups
Rosso, M
SYMETRIES QUANTIQUES: LXIVTH SESSION OF THE LES HOUCHES SUMMER SCHOOL, 1998, : 757 - 785
[8] Braid groups are linear groups
Bachmuth, S
ADVANCES IN MATHEMATICS, 1996, 121 (01) : 50 - 61
[9] ON BRAID GROUPS
BIRMAN, JS
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1969, 22 (01) : 41 - &
[10] On braid groups
Dubrovina, TV
Dubrovin, NI
SBORNIK MATHEMATICS, 2001, 192 (5-6) : 693 - 703

← 1 2 3 4 5 →