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Examples of Large Centralizers in the Artin Braid Groups
Geometriae Dedicata, 2004N. Franco and J. González-Meneses made the following conjecture: The normalizer of an element of the Artin braid group \(B_n\) on \(n\) strings is generated by no more than \(n-1\) elements. The `normalizer' of an element of a group is defined as the subgroup of all elements commuting with it; this subgroup is often also called the `centralizer' of the
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Braid groups, Artin groups and their applications in cryptography
2009The aim of this article is to show how the braid groups can serve as a good platform to enrich cryptography. Braid groups are useful to cryptography for a number of reasons: (i) the word problem is solved via a fast algorithm which computes the canonical form which can be efficiently handled by computers, (ii) an algorithm which computes an unfaithful ...
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Dynamical cocycles with values in the Artin braid group
1997By considering the way an n-tuple of points in the 2-disk are linked together under iteration of an orientation preserving diffeomorphism, we construct a dynamical cocycle with values in the Artin braid group. We study the asymptotic properties of this cocycle and derive a series of topological invariants for the diffeomorphism which enjoy rich ...
Gambaudo, Jean-Marc +1 more
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Majorana fermions and representations of the artin braid group
Quantum Information Science, Sensing, and Computation X, 2018In this paper we study unitary braid group representations associated with Majorana Fermions. Majorana Fermions are represented by Majorana operators, elements of a Clifford algebra. The paper recalls and proves a general result about braid group representations associated with Clifford algebras, and compares this result with the Ivanov braiding ...
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Representations of Artin’s braid groups and linking numbers of periodic orbits
Journal of Knot Theory and Its Ramifications, 1995Let P be a periodic orbit of period n≥3 of an orientation-preserving homeomorphism f of the 2-disc. Let q be the least integer greater than or equal to n/2−1. Then f admits a periodic orbit Q of period less than or equal to q such that the linking number of P about Q is non-zero.
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On a canonical lift of Artin's representation to loop braid groups
Journal of Pure and Applied Algebra, 2021Celeste Damiani
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Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups
Proceedings of the London Mathematical Society, 1999Patrick Dehornoy
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The Temperley-Lieb Algebra and the Artin Braid Group
2023Józef H. Przytycki +4 more
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ARTIN'S BRAID GROUPS, FREE GROUPS, AND THE LOOP SPACE OF THE 2-SPHERE
Quarterly Journal of Mathematics, 2011F R Cohen, Jie Wu
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On parabolic subgroups of Artin–Tits groups of spherical type
Advances in Mathematics, 2019María Cumplido +2 more
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