Results 11 to 20 of about 285 (147)
Generalizations of the standard Artin representation are unitary [PDF]
International Journal of Mathematics and Mathematical Sciences, 2005 We consider the Magnus representation of the image of the braid group under the generalizations of the standard Artin representation discovered by M. Wada.
Mohammad N. Abdulrahim
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, 2023 We show that the Lawrence--Krammer representation can be obtained as the quantization of the symmetric square of the Burau representation. This connection allows us to construct new representations of braid groupsComment: The following "Theorem 3.1.
Kosyak, Alexandre
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On the Burau representation of $B_3$ modulo $p$
We present an algorithm that, given a prime $p$ as input, determines whether or not the Burau representation of the 3-strand braid group modulo $p$ is faithful. We also prove that the representation is indeed faithful when $p\le 13$.
Lee, Donsung
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The homology polynomial and the burau representation for pseudo-anosov braids
, 2021 The homology polynomial is an invariant for pseudo-Anosov mapping classes (Birman, 2010). We study the homology polynomial as an invariant for pseudo-Anosov braids and its connection tothe Burau representation.
Shultz, Warren Michael
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Invariants of colored links and generalizations of the Burau representation
, 2017 Cette thèse se concentre sur la topologie de basse dimension et plus spécifiquement sur la théorie des noeuds. Elle se décompose en trois parties consacrées respectivement aux invariants d'entrelacs colorés, à la représentation de Burau du groupe de ...
Conway, Anthony
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Salter's question on the image of the Burau representation of $B_3$
In 1974, Birman posed the question of under what conditions a matrix with Laurent polynomial entries is in the image of the Burau representation. In 1984, Squier observed that the matrices in the image are contained in a unitary group.
Lee, Donsung
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On the irreducibility of the extensions of Burau and Gassner representations [PDF]
ANNALI DELL'UNIVERSITA' DI FERRARA, 2021 We study the $n$th degree representations $\hat{ρ_G}$ of $Cb_{n}$ and $\hat{ρ_B}$ of $C_{n}$, defined by Valerij G. Bardakov, where $Cb_{n}$ is the group of basis conjugating automorphisms and $C_n$ is the group of conjugating automorphisms. We prove that $\hat{ρ_G}$ is reducible and its $(n-1)$th degree composition factor $\hat{ϕ_G}$ is irreducible if
Mohamad N. Nasser +1 more
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On the Burau representation of B 4 modulo p [PDF]
, 2021 The problem of faithfulness of the (reduced) Burau representation for $n =4$ is known to be equivalent to the problem of whether certain two matrices $A$ and $B$ generate a free group of rank two. It is known that $A^3$ and $B^3$ generate a free group of rank two \cite{9}, \cite{10}, \cite{4}.
Beridze, A., Bigelow, S., Traczyk, P.
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Schur–Weyl duality for tensor powers of the Burau representation [PDF]
Research in the Mathematical Sciences, 2021 Artin's braid group $B_n$ is generated by $σ_1, \dots, σ_{n-1}$ subject to the relations \[ σ_i σ_{i+1} σ_i = σ_{i+1} σ_i σ_{i+1}, \quad σ_iσ_j = σ_j σ_i \text{ if } |i-j|>1. \] For complex parameters $q_1,q_2$ such that $q_1q_2 \ne 0$, the group $B_n$ acts on the vector space $\mathbf{E} = \sum_i \mathbb{C} \mathbf{e}_i$ with basis $\mathbf{e}_1 ...
Stephen Doty, Anthony Giaquinto
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Security analysis of key agreement protocol based on matrix power function
Lietuvos Matematikos Rinkinys, 2012 Key agreement protocol (KAP) using Burau braid groups representation and matrix power function (MPF) is analyzed. MPF arguments are Burau representation matrices defined over finite field or ring.
Paulius Vitkus, Eligijus Sakalauskas
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