The Braid Group
MONODROMY REPRESENTATION OF THE BRAID GROUP
... Kohno and Drinfel’d. Such representations are typically referred to as monodromy representations of the braid group along solutions of the KZ equation. These linear representations are of great interest ...
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The Interplay between Linear Representations of the Braid Group
... the braid group, B n , on the free group with n ...free group, G nm , of rank nm, we compose Cohen’s map B n → B nm and the embedding B nm → Aut(G nm ) via Wada’s ...
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New rewriting system for the braid group B 4
... a group word in t 1 , t 2 ...the braid group presenta- tion (2) with cyclically presented groups (in sense of Johnson ...the group B 3 0 = ht 1 , t 2 ...following group presentation ...
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Fock parafermions and self-dual representations of the braid group
... The outline of the paper follows. In Section 2 we present the Weyl algebra with generators U and V originally introduced to study finite-dimensional quantum mechanics. There we show a fundamental canonical decomposition ...
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On an authentication scheme based on the Root Problem in the braid group
... ROOT PROBLEM IN THE BRAID GROUP BOAZ TSABAN Abstract. Lal and Chaturvedi proposed two authentication sche- mes presumably based on the difficulty of the Root Problem in the braid group. We ...
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ON THE FAITHFULNESS OF JONES-WENZL REPRESENTATION OF THE BRAID GROUP $B_{4}$
... In [4], H. Haidar and M. Abdulrahim constructed a representation of P 3 , the pure braid group on three strands. They studied its irreducibility and unitarity as a tool to study its faithfulness in the ...
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A Study of Topological Invariants in the Braid Group B2
... a braid with all positive crossings because any word in B 2 can be reduced to a word with all positive, negative, or no ...this braid, where the first crossing was all the same color, we would get a ...
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Krammer's Representation of the Pure Braid Group, P3
... pure braid group on three strings: P 3 → GL3, Zt ±1 , q ±1 , where t and q are ...the braid group, B 3 , we specialize the indeterminates t and q to nonzero complex ...pure braid ...
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Contractible stability spaces and faithful braid group actions
... the braid group Br (Q) acts freely upon it by spherical twists, in particular that the spherical twist group Br (Γ N Q) is isomorphic to Br ...Grothendieck group and discrete derived ...
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On the Irreducibility of Fourth Dimensional Tuba's Representation of the Pure Braid Group on Three Strands
... pure braid group on three ...the braid group , namely the pure braid group, we get the following representation of dimension d = ...
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An Introduction to Braid Theory
... 5 The word and conjugacy problems on B n The braid group is an extremely efficient way to represent braids, and has already yielded many interesting and useful results. However, we now move on to show that ...
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Braid Group Representations from Braiding Gapped Boundaries of Dijkgraaf-Witten Theories. Nicolás Escobar Velásquez
... This document is organized as follows. Chapter 2 presents some basic results about monoidal and braided categories, as well as the braid group and Lagrangian algebras. Chap- ter 3 contains the main results ...
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The Multivariable Alexander Polynomial for a Closed Braid
... closed braid and axis, leading at once to the polynomial of the closed ...pure braid the resulting matrix is conjugate to a reduced version of the Gassner matrix the construction given here has the ...
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New proposals for the popularization of braid theory
... The chapters last about 15 minutes, a time after which attention can sink. Each part is symbolized by an object: the first one is represented by a book. Here braids are introduced as mathematical objects and the ...
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Mutual braiding and the band presentation of braid groups
... closed braid and its axis are `mutually braided' in the sense of Rudolph ...the braid axis. We show how such a braid can be presented naturally as a word in the `band generators' of the braid ...
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Braid subgroup normalisers, commensurators and induced representations
... classical braid groups of ...the braid group B n in B m , n ≤ m ≤ ...class group of the m-punctured 2-dimensional ...geometric braid subgroups (Theorem ...class group, upon ...
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A Practical Attack on the Root Problem in Braid Groups
... on braid groups have been ...in braid groups gained attention, and in the sequel we show that parame- ters proposed in this context succumb to a simple heuristic ...the braid group B n to a ...
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Towards Generating Secure Keys for Braid Cryptography
... the braid group is to write a braid word in its weighted ...of braid words, braids are coded in their unique weighted ...a braid generated by multiplying random ...random braid ...
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Local representations of the loop braid group
... TQFTs are muh harder to onstrut, and the largest known expliit lass is the Crane- Yetter TQFTs based on pre-modular ategories [11, 34℄. The diÆulty of onstruting interesting representations of the loop braid ...
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On Artin's braid group and polyconvexity in the calculus of variations
... trivial braid ε n , it must be that one of the three possibilities listed above occurs in the product; by removing the corresponding word (which is of length either 2, 4 or 6) one arrives at a new product that is ...
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