Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

On the Faithfulness of the Extension of Lawrence-Krammer Representation of the Group of Conjugating Automorphisms C3


Affiliations
1 Department of Mathematics and Computer Science, Beirut Arab University, P.O. Box 11-5020, Beirut, Lebanon
     

   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
Notifications
Font Size


  • 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: 275

PDF Views: 0




  • On the Faithfulness of the Extension of Lawrence-Krammer Representation of the Group of Conjugating Automorphisms C3

Abstract Views: 275  |  PDF Views: 0

Authors

Mohamad N. Nasser
Department of Mathematics and Computer Science, Beirut Arab University, P.O. Box 11-5020, Beirut, Lebanon
Mohammad N. Abdulrahim
Department of Mathematics and Computer Science, Beirut Arab University, P.O. Box 11-5020, Beirut, Lebanon

Abstract


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.

References





DOI: https://doi.org/10.18311/jims%2F2023%2F29869