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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 22 for “"braid group"”.
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The Pure Virtual Braid Group is Quadratic
… for grK to be quadratic. When K is the group algebra of a group G, quadraticity is known to be equivalent to the existence of a (not necessarily homomorphic) universal finite type invariant for G. Thus the PVH Criterion also implies the existence of a universal finite type invariant for …
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Solutions to the conjugacy search and decision problems in the braid group using finite conjugacy class invariants
For two braids, A, B ∈ Bn, the conjugacy decision problem asks whether another braid X ∈ Bn exists such that X−1 A X = B. If we know A, B ∈ Bn are indeed conjugate, the conjugacy search problem asks us to find a braid Y ∈ Bn such that Y −1 A Y = B. In this dissertation we investigate a number of …
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A Structure-based Attack on the Linearized Braid Group-based Diffie-Hellman Conjugacy Problem in Combination with an Attack using Polynomial Interpolation and the Chinese Remainder Theorem
… improve a linear algebra attack on the so-called braid group-based Diffie-Hellman conjugacy problem (BDHCP). The general procedure of the attack is to transform a BDHCP to the problem of solving several simultaneous matrix equations. A first improvement is achieved by reducing the solution space …
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From Homological Algebra To Topology via Type B Zigzag Algebra and Heisenberg Algebra
… a faithful categorical action of the type $B$ braid group on the bounded homotopy category of finitely generated projective modules over a finite dimensional algebra which we call the type $B$ zigzag algebra. This categorical action is closely related to the action of the type $B$ braid group …
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From Homological Algebra To Topology via Type B Zigzag Algebra and Heisenberg Algebra
… a faithful categorical action of the type $B$ braid group on the bounded homotopy category of finitely generated projective modules over a finite dimensional algebra which we call the type $B$ zigzag algebra. This categorical action is closely related to the action of the type $B$ braid group …
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Constructing Hecke-type Structures, their Representations and Applications
… structure called the double a�ne Q-dependent braid group. The signi�cance of this structure is that it is located at the top level of the hierarchy of all other structures that are known to be related to the braid group. In particular, as specialisations we obtain the Hecke algebra, in …
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Topological field theories and fractional statistics
… of determining which representations of the braid group on a Riemann surface are carried by the wave function of a quantized Abelian Chern-Simons theory interacting with non-dynamical matter. We generalize the quantization of Chern-Simons theory to the case where the coefficient of the …
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GT-shadows related to finite quotients of the full modular group
… of the mysterious Grothendieck-Teichmueller group GT introduced by V. Drinfeld in 1990 [5]. GT-shadows [4] form a groupoid whose objects are certain finite index normal subgroups of Artin’s braid group B4 on 4 strands. In this thesis we introduce GT-shadows for the gentle version GTgen of the …
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Least dilatation of pure surface braids
… classification of the mapping class group, a result that is fundamental to the field of low dimensional topology. In particular, Thurston's work gives us a powerful normal form for mapping classes: up to taking powers and restricting to subsurfaces, every mapping class can be …
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Braid Groups on Graphs
… the tree T from a given four strand tree braid group B 4T up to homeomorphism. Thus tree braid groups B4T and trees T (up to homeomorphism) are in bijective correspondence. We use this bijection to solve a version of the isomorphism problem for tree braid groups with n = 4 strands.
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Knot Floer Homology and Categorification
… of twisted Soergel bimodules and construct a braid group action on the homotopy category of complexes of twisted Soergel bimodules. We prove that the category of twisted Soergel bimodules categorifies the Hecke algebra with an extra indeterminate and its inverse adjoined. The braid group …
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Braid groups and mapping class groups for 2-orbifolds
… achievement of this thesis is that pure orbifold braid groups fit into an exact sequence 1$\\rightarrow$ …
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On the Combinatorics of Certain Garside Semigroups
… to the word and conjugacy problems in the braid group on n-strands, using a particular element that he called the fundamental word. Others have since defined fundamental words in the generalized setting of Artin groups, and even more recently in Garside groups. We consider the problem of …
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Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras
… the affine flag manifold (for the Langlands dual group). We prove results relating all three of these categorifications, and use them to deduce nontrivial equivalences of categories. In addition, our main theorem allows us to deduce the existence of a strict braid group action on all of the …
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Optimising Qubit Designs for Topological Quantum Computation
… computations, are governed by the exchange group of the constituent particles. We examine representations of these exchange groups and investigate what restrictions their structure places on the effciency, reliability and universality of qubits (and multi-qubit systems) as a function of the …
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Quantum Toroidal Superalgebras
… are isomorphic, an action of the toroidal braid group is constructed. The superalgebra E(s) contains two distinguished subalgebras, both isomorphic to the quantum affine superalgebra Uq sl̂(m|n) with parity "s", called vertical and horizontal subalgebras. We show the existence of Miki …
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Quantized multiplicative quiver varieties and actions of higher genus braid groups
… H, and yields representations of the elliptic braid group of rank n.
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On representations of rational Cherednik algebras
… appearing in the representation theory of finite groups of Lie type. In particular, irreducible representations in the rational Cherednik category O with particular generalized support conditions correspond to irreducible representations of associated generalized Hecke algebras. An explicit …
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A Coherent Categorification of the Asymptotic Affine Hecke Algebra
… classes associated to Bezrukavnikov–Riche’s braid group action for the Springer resolution. In particular, we obtain that the coherent Springer sheaf lies in cohomological degree 0 (i.e., is a sheaf rather than a complex), resolving a conjecture of Ben-Zvi–Chen–Helm–Nadler and Zhu. As a …
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Coherent sheaves on varieties arising in Springer theory, and category 0
… weights for an arbitrary simple algebraic group H, and 0, the set of pairs consisting of a nilpotent orbit and a finite-dimensional irreducible representation of the isotropy group of the orbit (as originally conjectured by Lusztig and Vogan). Here we prove an analogous statement for the …
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