The Alexander- And Jones-Invariants And The Burau Module
, 1995 . From the braid-valued Burau module over the braid group we construct the Yang-Baxter matrices yielding the Alexander- and the Jones knot invariants. This generalises an observation of V. F. R. Jones. 1. Introduction It has been known for long that the
Florin Constantinescu +3 more
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Extensions of Tong-Yang-Ma representation
, 2023 In 1996, Tong, Yang and Ma defined a family of representations of the braid group which have the same dimensions as the (unreduced) Burau representations but are not equivalent.
Takano, Akihiro, Soulié, Arthur
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COVID-19 and healthcare worker mental well-being: Comparative case studies on interventions in six countries. [PDF]
Health Policy, 2023 Byrne JP +3 more
europepmc +1 more source
Some remarks about the faithfulness of the Burau representation of Artin--Tits groups
Comments welcome!We discuss the extension of the faithfulness question for the Burau representation of braid groups to the case of Artin--Tits groups. We prove that the Burau representation is not faithful in affine type $\tilde{A_3}$, and not faithful ...
Bapat, Asilata, Queffelec, Hoel
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A Lagrangian representation of tangles
, 2005 We construct a functor from the category of oriented tangles in ${\Bbb R}^3$ to the category of Hermitian modules and Lagrangian relations over ${\Bbb Z}[t,t^{-1}]$. This functor extends the Burau representation of the braid groups and its generalization
Turaev, Vladimir
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On the Burau representation of the braid group $B_4$
, 2020 In this thesis, we establish strong constraints on the kernel of the (reduced) Burau representation $\beta_4:B_4\to \text{GL}_3\left(\mathbb{Z}\left[q^{\pm 1}\right]\right)$ of the braid group $B_4$, addressing a conjecture originally posed in the 1930s.
Datta, Amitesh
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Material Coherence from Trajectories via Burau Eigenanalysis of Braids
, 2019 In this paper, we provide a numerical tool to study material coherence from a set of 2D Lagrangian trajectories sampling a dynamical system, i.e., from the motion of passive tracers.
Melissa Yeung +5 more
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Associations between perceived racial discrimination, racial residential segregation, and cancer screening adherence among low-income African Americans: a multilevel, cross-sectional analysis. [PDF]
Ethn Health, 2023 Ibekwe LN +4 more
europepmc +1 more source
Burau representation, Squier's form, and non-Abelian anyons
CoRRWe introduce a frequency-tunable, two-dimensional non-Abelian control of operation order constructed from the reduced Burau representation of the braid group $B_3$, specialised at $t=e^{iω}$ and unitarized by Squier's Hermitian form. Coupled to two non-commuting qubit unitaries $A$, $B$, the resulting switch admits a closed expression for the single ...
openaire +2 more sources
THE FAITHFULNESS QUESTION FOR THE BURAU REPRESENTATION
We consider the Burau and Gassner representations of the braid groups B(n). A sufficient condition for faithfulness, involving just a pair of arcs, is shown to be necessary as well for all but at most two values of n.
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