Results 21 to 30 of about 267 (215)

Topological model of composite fermions in the cyclotron band generator picture: New insights

Results in Physics, 2018
A combinatorial group theory in the braid groups is correlated with the unusual “anyon” statistic of particles in 2D Hall system in the fractional quantum regime well.
Beata Staśkiewicz
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HILDEN BRAID GROUPS

Journal of Knot Theory and Its Ramifications, 2012
Let Hgbe a genus g handlebody and MCG2n( Tg) be the group of the isotopy classes of orientation preserving homeomorphisms of Tg= ∂ Hg, fixing a given set of 2n points. In this paper we study two particular subgroups of MCG2n( Tg) which generalize Hilden groups defined by Hilden in [Generators for two groups related to the braid groups, Pacific J.
Bellingeri, P, CATTABRIGA, ALESSIA
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UNIVERSAL REPRESENTATIONS OF BRAID AND BRAID-PERMUTATION GROUPS [PDF]

Journal of Knot Theory and Its Ramifications, 2009
Drinfel'd used associators to construct families of universal representations of braid groups. We consider semi-associators (i.e. we drop the pentagonal axiom and impose a normalization in degree one). We show that the process may be reversed, to obtain semi-associators from universal representations of 3-braids.
Berceanu, Barbu, Papadima, Ştefan
openaire   +3 more sources

Krammer's Representation of the Pure Braid Group, 𝑃3

International Journal of Mathematics and Mathematical Sciences, 2010
We consider Krammer's representation of the pure braid group on three strings: 𝑃3→𝐺𝐿(3,𝑍[𝑡±1,𝑞±1]), where 𝑡 and 𝑞 are indeterminates. As it was done in the case of the braid group, 𝐵3, we specialize the indeterminates 𝑡 and 𝑞 to nonzero complex numbers ...
Mohammad N. Abdulrahim, Madline Al-Tahan
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A Graphical Calculus for Quantum Computing with Multiple Qudits using Generalized Clifford Algebras [PDF]

Quantum
In this work, we develop a graphical calculus for multi-qudit computations with generalized Clifford algebras, building off the algebraic framework developed in our prior work.
Robert Lin
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Attack on Kayawood protocol: uncloaking private keys

Journal of Mathematical Cryptology, 2020
We analyze security properties of a two-party key-agreement protocol recently proposed by I. Anshel, D. Atkins, D. Goldfeld, and P. Gunnels, called Kayawood protocol.
Kotov Matvei, Menshov Anton, Ushakov Alexander   +2 more
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On the Unitary Representations of the Braid Group B₆

Mathematics, 2019
We consider a non-abelian leakage-free qudit system that consists of two qubits each composed of three anyons. For this system, we need to have a non-abelian four dimensional unitary representation of the braid group B 6 to obtain a totally ...
Malak M. Dally, Mohammad N. Abdulrahim
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New Construction of Blind Signatures From Braid Groups

IEEE Access, 2019
A new construction of a blind signature scheme based on braid groups is proposed. In the random oracle model, the proposed scheme is provably unforgeable against chosen message attacks, assuming that the one-more matching conjugate problem in braid ...
Licheng Wang, Yanmei Tian, Yun Pan, Yixian Yang   +3 more
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On groups Gnk, braids and Brunnian braids [PDF]

Journal of Knot Theory and Its Ramifications, 2016
In [V. O. Manturov, arXiv:1501.05208v1 ], the second author defined the [Formula: see text]-free braid group with [Formula: see text] strands [Formula: see text]. These groups appear naturally as groups describing dynamical systems of [Formula: see text] particles in some “general position”. Moreover, in [V. O. Manturov and I. M. Nikonov, J.
Kim, Seongjeong, Manturov, V. O.
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Generalizations of the standard Artin representation are unitary

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
doaj   +1 more source