EXTENDING REPRESENTATIONS OF BRAID GROUPS TO THE AUTOMORPHISM GROUPS OF FREE GROUPS

DOI10.1142/S0218216505004251zbMath1085.20017arXivmath/0408330MaRDI QIDQ3373065

Valeriy G. Bardakov

Publication date: 13 March 2006

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0408330

zbMATH Keywords

pure braid groupsArtin braid groupsBurau representationIA-automorphisms of free groupsfaithful linear representationsGassner representationgroups of conjugating automorphisms

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Braid groups; Artin groups (20F36) Topological methods in group theory (57M07) Automorphism groups of groups (20F28) Free nonabelian groups (20E05)

Related Items (12)

Low-dimensional representations of the three component loop braid group ⋮ The Burau representations of loop braid groups ⋮ A journey through loop braid groups ⋮ Generalisations of Hecke algebras from loop braid groups ⋮ ABELIAN AND METABELIAN QUOTIENT GROUPS OF SURFACE BRAID GROUPS ⋮ Unnamed Item ⋮ LOCAL REPRESENTATIONS OF THE LOOP BRAID GROUP ⋮ Representations of the loop braid groups from braided tensor categories ⋮ On the irreducibility of the extensions of Burau and Gassner representations ⋮ CLASSIFICATION OF CLOSED VIRTUAL 2-BRAIDS ⋮ On the Pure Virtual Braid GroupPV₃ ⋮ A note on representations of welded braid groups

Cites Work

• Unnamed Item
• Über Zopfgruppen und gleichsinnig verdrillte Verkettungen
• The Burau representation is not faithful for \(n=5\)
• The Burau representation is not faithful for \(n\geq 6\)
• On Basis-Conjugating Automorphisms of Free Groups
• The Burau representation of the braid group 𝐵_{𝑛} is unfaithful for large 𝑛
• Braid groups are linear
• Braid groups are linear

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