Abstract commensurators of braid groups
Christopher J. Leininger, Dan Margalit
Abstract
Let Bn be the braid group on n strands, with n at least 4, and let Mod(S) be the extended mapping class group of the sphere with n+1 punctures. We show that the abstract commensurator of Bn is isomorphic to a semidirect product of Mod(S) with a group we refer to as the transvection subgroup, Tv(Bn). We also show that Tv(Bn) is itself isomorphic to a semidirect product of an infinite dimensional rational vector space with the multiplicative group of nonzero rational numbers.
Create a lesson
Related papers
The variety generated by all additively idempotent semirings of order four
Mengya Yue, Xiaolei Shao
Generation of Iterated Wreath Products Constructed from Full Transformation Monoids and Symmetric Groups
Jiaping Lu
Kernel--wreath constructions and infinite families of finite simple skew braces
Marco Damele
Explicit equational bases for the power semirings of S7
Mengya Yue, Miaomiao Ren, Zidong Gao
The free multiplicative Lie algebra L(P) for a finitely generated parafree group P
Dessislava H. Kochloukova
An order automorphism of a Dlab group not induced by conjugation
Ting Gong, Yong Yang, Michael Ruofan Zeng