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THE BRAID GROUP AND OTHER GROUPS [PDF]
The Quarterly Journal of Mathematics, 1969 F. Garside
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A Categorical Model for the Virtual Braid Group [PDF]
, 2011 This paper gives a new interpretation of the virtual braid group in terms of a strict monoidal category SC that is freely generated by one object and three morphisms, two of the morphisms corresponding to basic pure virtual braids and one morphism ...
Kauffman, Louis H., Lambropoulou, Sofia
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Braid group action on the module category of quantum affine algebras [PDF]
, 2020 Let $\mathfrak{g}_0$ be a simple Lie algebra of type ADE and let $U'_q(\mathfrak{g})$ be the corresponding untwisted quantum affine algebra. We show that there exists an action of the braid group $B(\mathfrak{g}_0)$ on the quantum Grothendieck ring $K_t(\
M. Kashiwara +3 more
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Higher Braid Groups and Regular Semigroups from Polyadic-Binary Correspondence
Mathematics, 2021 In this note, we first consider a ternary matrix group related to the von Neumann regular semigroups and to the Artin braid group (in an algebraic way).
Steven Duplij
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Mathematics, 2023 In this paper, by introducing an isomorphism from the Mihailova subgroup of F2×F2 to the Mihailova subgroups of a braid group, we give an explicit presentation of Mihailova subgroups of a braid group.
Hanling Lin, Xiaofeng Wang, Min Li
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A Faithful Braid Group Action on the Stable Category of Tricomplexes [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2019 Bicomplexes of vector spaces frequently appear throughout algebra and geometry. In Section 2 we explain how to think about the arrows in the spectral sequence of a bicomplex via its indecomposable summands. Polycomplexes seem to be much more rare.
M. Khovanov, You Qi
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Representation stability in the level 4 braid group [PDF]
Mathematische Zeitschrift, 2019 We investigate the cohomology of the level 4 subgroup of the braid group, namely, the kernel of the mod 4 reduction of the Burau representation at t=-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts ...
Kevin Kordek, D. Margalit
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BRAID GROUP ACTION AND ROOT VECTORS FOR THE q-ONSAGER ALGEBRA [PDF]
Transformation groups, 2017 We define two algebra automorphisms Ͳ0 and Ͳ1 of the q-Onsager algebra Bc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek ...
P. Baseilhac, S. Kolb
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Burau Representation of Braid Groups and q-Rationals [PDF]
International mathematics research notices, 2023 We establish a link between the new theory of $q$-deformed rational numbers and the classical Burau representation of the braid group ${\mathcal {B}}_{3}$.
S. Morier-Genoud +2 more
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Key agreement protocol in Braid group representation level
Lietuvos Matematikos Rinkinys, 2021 In this paper the key agreement protocol is given and the applicationof it in Braid groups is suggested. The one way of protocol is being justified.
Povilas Tvarijonas +2 more
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