A new family of infinitely braided Thompson's groups

Julio Aroca; María Cumplido

doi:10.1016/j.jalgebra.2020.07.021

A new family of infinitely braided Thompson's groups

Julio Aroca
, María Cumplido^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

229 Downloads (Pure)

Abstract

We present a generalization of the Dehornoy-Brin braided Thompson group BV₂ that uses recursive braids. Our new groups are denoted by BV_n,r(H), for all n≥2,r≥1 and H≤B_n, where B_n is the braid group on n strands. We give a new approach to deal with braided Thompson groups by using strand diagrams. We show that BV_n,r(H) is finitely generated if H is finitely generated.

Original language	English
Pages (from-to)	5-34
Number of pages	30
Journal	Journal of Algebra
Volume	607
Issue number	Part B
Early online date	5 Aug 2020
DOIs	https://doi.org/10.1016/j.jalgebra.2020.07.021
Publication status	Published - 1 Oct 2022

Keywords

Braid groups
Rewriting systems
Strand diagrams
Thompson groups

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2020.07.021

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title = "A new family of infinitely braided Thompson's groups",

abstract = "We present a generalization of the Dehornoy-Brin braided Thompson group BV2 that uses recursive braids. Our new groups are denoted by BVn,r(H), for all n≥2,r≥1 and H≤Bn, where Bn is the braid group on n strands. We give a new approach to deal with braided Thompson groups by using strand diagrams. We show that BVn,r(H) is finitely generated if H is finitely generated.",

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N2 - We present a generalization of the Dehornoy-Brin braided Thompson group BV2 that uses recursive braids. Our new groups are denoted by BVn,r(H), for all n≥2,r≥1 and H≤Bn, where Bn is the braid group on n strands. We give a new approach to deal with braided Thompson groups by using strand diagrams. We show that BVn,r(H) is finitely generated if H is finitely generated.

AB - We present a generalization of the Dehornoy-Brin braided Thompson group BV2 that uses recursive braids. Our new groups are denoted by BVn,r(H), for all n≥2,r≥1 and H≤Bn, where Bn is the braid group on n strands. We give a new approach to deal with braided Thompson groups by using strand diagrams. We show that BVn,r(H) is finitely generated if H is finitely generated.

KW - Braid groups

KW - Rewriting systems

KW - Strand diagrams

KW - Thompson groups

UR - https://www.scopus.com/pages/publications/85089380020

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DO - 10.1016/j.jalgebra.2020.07.021

M3 - Article

AN - SCOPUS:85089380020

SN - 0021-8693

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SP - 5

EP - 34

JO - Journal of Algebra

JF - Journal of Algebra

IS - Part B

ER -

A new family of infinitely braided Thompson's groups

Abstract

Keywords

ASJC Scopus subject areas

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