Results 41 to 50 of about 2,228 (168)

A polynomial algorithm for the braid double shielded public key cryptosystems

Қарағанды университетінің хабаршысы. Математика сериясы, 2016
We propose new provable practical deterministic polynomial time algorithm of cryptographic analysis for the braid Wang, Xu, Li, Lin and Wang «Double shielded public key cryptosystems», where the authors recommended the Artin braid groups Bn as platforms
V.A. Roman’kov
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Ising-like and Fibonacci anyons from KZ-equations

Journal of High Energy Physics, 2022
In this work we present solutions to Knizhnik-Zamolodchikov (KZ) equations corresponding to conformal block wavefunctions of non-Abelian Ising-like and Fibonacci Anyons.
Xia Gu, Babak Haghighat, Yihua Liu
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Braid groups are linear [PDF]

Journal of the American Mathematical Society, 2000
The braid group B n B_n can be defined as the mapping class group of the n n -punctured disk. A group is said to be linear if it admits a faithful representation into a group of matrices over R \mathbf R .
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Topology and Algebra of Bonded Knots and Braids

Mathematics
In this paper we present a detailed study of bonded knots and their related structures, integrating recent developments into a single framework. Bonded knots are classical knots endowed with embedded bonding arcs modeling physical or chemical bonds.
Ioannis Diamantis, Louis H. Kauffman, Sofia Lambropoulou   +2 more
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Iterant Algebra

Entropy, 2017
We give an exposition of iterant algebra, a generalization of matrix algebra that is motivated by the structure of measurement for discrete processes. We show how Clifford algebras and matrix algebras arise naturally from iterants, and we then use this ...
Louis H. Kauffman
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Yang-Yang functions, monodromy and knot polynomials

Journal of High Energy Physics, 2021
We derive a structure of ℤ[t, t −1]-module bundle from a family of Yang-Yang functions. For the fundamental representation of the complex simple Lie algebra of classical type, we give explicit wall-crossing formula and prove that the monodromy ...
Peng Liu, Wei-Dong Ruan
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On marked braid groups

Journal of Knot Theory and Its Ramifications, 2015
In this paper, we introduce [Formula: see text]-braids and, more generally, [Formula: see text]-braids for an arbitrary group [Formula: see text]. They form a natural group-theoretic counterpart of [Formula: see text]-knots, see [V. O. Manturov; Reidemeister moves and groups, preprint (2014), arXiv:1412.8691].
Fedoseev, Denis A., Manturov, Vassily O., Cheng, Zhiyun   +2 more
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Relative Nielsen Numbers, Braids and Periodic Segments

Advanced Nonlinear Studies, 2017
The aim of this paper is to establish a connection between the method of period segments and the relative Nielsen fixed point theory. We prove that if W is a periodic segment over [0,T]{[0,T]} for the T-periodic semi-process Φ, then the Poincaré map P ...
Wójcik Klaudiusz
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Quasi-morphisms on the group of area-preserving diffeomorphisms of the $2$-disk via braid groups

Proceedings of the American Mathematical Society, Series B, 2014
Recently Gambaudo and Ghys proved that there exist infinitely many quasi-morphisms on the group 𝐷𝑖𝑓𝑓_{Ω}^{∞}(𝐷²,∂𝐷²) of area-preserving diffeomorphisms of the 2-disk 𝐷².
Tomohiko Ishida
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Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension

SciPost Physics
Anyons obeying fractional exchange statistics arise naturally in two dimensions: Hard-core two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent exchange paths can be
Sebastian Nagies, Botao Wang, Adam C. Knapp, André Eckardt, Nathan L. Harshman
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