Open Access
Subscription Access
Open Access
Subscription Access
On the Faithfulness of the Extension of Lawrence-Krammer Representation of the Group of Conjugating Automorphisms C3
Subscribe/Renew Journal
Let Cn be the group of conjugating automorphisms. We study the representation ρ of Cn, an extension of Lawrence-Krammer representation of the braid group Bn. It is known that the representation ρ is unfaithful for n ≥ 5, the cases n = 3, 4 remain open. In our work, we make attempts towards the faithfulness of ρ in the case n = 3.
Keywords
Braid Group, Free Group, Lawrence–Krammer Representation, Burau Representation, Faithfulness.
Subscription
Login to verify subscription
User
Font Size
Information
- Valerij G. Bardakov, The structure of the group of conjugating automorphisms and the linear representation of the braid groups of some manifolds, Algebra i Logika, 42 (5)(2003), 515–541.
- S. Bigelow, Braid groups are linear, J. Amer. Math. Soc., 14 (2001), 471–486.
- J. S. Birman, Braids, links and mapping class groups, Annals of Mathematical studies, (8), Rrinceton University Press, 1974.
- D. Krammer, Braid groups are linear, Annals Math., 155 (1)(2002), 131–156.
- A. G. Savushkina, On group of conjugating automorphisms of free groups, Matem. Zametki, 60 (1)(1996), 92–108 (in Russian).
Abstract Views: 295
PDF Views: 0