131,447 research outputs found
Multipartite d-level GHZ bases associated with generalized braid matrices
No full textWe investigate the generalized braid relation for an arbitrary multipartite d-level system and its application to quantum entanglement. By means of finite-dimensional representations of quantum plane algebra, a set of unitary matrix representations satisfying the generalized braid relation can be constructed. Such generalized braid matrices can entangle N-partite d-level quantum states. Applying the generalized braid matrices on the standard basis of product states, one can obtain a set of maximally entangled bases. Further study shows that such entangled states can be viewed as the N-partite d-level Greenberger-Horne-Zeilinger (GHZ) states
Braid Groups and Evolution Algebras
No full textIn this paper, we explore the relationship between the braid group and
evolution algebras. First, we explore the braid group and how it is constructed. Next we discuss the Burau representation, and its relationship with free differential calculus and Magnus representations. Finally we use the Burau representation to create a new representation from the braid group directly to evolution algebras
Fracture Behavior of a 3-D Braid Graphite/Epoxy Composite
No full text An exploratory study of the fracture behavior and notch sensitivity of a 4-step, 3-D braid-reinforced graphite/epoxy composite has been made. Test methods based on the Mode I compact tension specimen were developed and lower bounds for the damage initiating force and the work of fracture were determined for certain notch-to-braid axis orientations. These values are higher than for laminate composites but showed severe anisotropy. Complementary in-situ and post-mortem optical and scanning electron microscopy were used to identify microstructural failure controlling features and to develop a volume-to-surface structural mapping strategy useful in accounting for some of the observed features of the failure process. </jats:p
Generalized braid group actions
No full textConsider a diagrammatic category whose objects are partitions of n and whose morphisms are braids with multiplicities where strands are allowed to merge and come apart, so topologically such a braid is a trivalent graph with boundary. In addition, we add framing on edges with multiplicities greater than 1. The usual (type A) braid group is then the group of automorphisms of (1,1,...,1). We prove that any DG enhanceable triangulated category D with a braid group action (of which there are numerous examples in algebraic geometry) can be completed to a representation of this diagrammatic category. We do this by constructing a monad over D that is best described as the nil Hecke algebra generated by the generators of the braid group action, and considering suitable categories of modules over its "block subalgebras". If D=D(X), those modules would be complexes of sheaves on X with additional data. Similar structures have been known before, but they satisfy stronger conditions (i.e. the twist of framing on a multiple strand being a shift, which in our construction is not the case). This is joint work in progress with Timothy Logvinenko.Non UBCUnreviewedAuthor affiliation: Kansas State UniversityResearche
Braid Groups and Evolution Algebras
No full textThesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.In this paper, we explore the relationship between the braid group and evolution algebras. First, we explore the braid group and how it is constructed. Next we discuss the Burau representation, and its relationship with free differential calculus and Magnus representations. Finally we use the Burau representation to create a new representation from the braid group directly to evolution algebras.MathematicsBachelors of Science (BS
Homology of braid groups and their generalizations
No full textIn the paper we give a survey of (co)homologies of braid groups and groups connected with them. Among these groups are pure braid groups and generalized braid groups. We present explicit formulations of some theorems of V. I. Arnold, E. Brieskorn, D. B. Fuks, F. Cohen, V. V. Goryunov and others. The ideas of some proofs are outlined. As an application of (co)homologies of braid groups we study the Thom spectra of these groups
REPRESENTATIONS OF BRAID GROUPS AND GENERALISATIONS
Get PDFFew misprints corrected, simpler proof for proposition 10We define and study extensions of Artin's representation and braid monodromy representation to the case of topological and algebraical generalisations of braid groups. In particular we provide faithful representations of braid groups of oriented surfaces with boundary components as (outer) automorphisms of free groups. We give also similar representations for braid groups of non oriented surfaces with boundary components and we show a representation of braid groups of closed surfaces as outer automorphisms of free groups. Finally, we provide faithful representations of Artin-Tits groups of type as automorphisms of free groups
Structure of braid graphs in simply-laced Coxeter systems
No full textAny two reduced expressions for the same Coxeter group element are related by a sequence of commutation and braid moves. We say that two reduced expressions are braid equivalent if they are related via a sequence of braid moves,and the corresponding equivalence classes are called braid classes. Each braid class can be encoded in terms of a braid graph in a natural way. In this thesis, we study the structure of braid graphs in simply-laced Coxeter systems. In a recent
paper, Awik et al. proved that every reduced expression has a unique factorization as a product of so-called links, which in turn induces a decomposition of the braid graph into a box product of the braid graphs for each link factor. For a special class of links, called Fibonacci links, they showed that the corresponding braid graph is isomorphic to a Fibonacci cube graph. In this thesis, we prove that every Fibonacci cube occurs as the braid graph for a link in any simply-laced triangle-free Coxeter System whose corresponding braid graph contains the Coxeter graph of the Coxeter system of type ÇD
4 as a subgraph
The inverse braid monoid
No full textAbstractWe introduce an inverse monoid which plays a similar role with respect to the symmetric inverse semigroup that the braid group plays with respect to the symmetric group
Explicit Presentations for the Dual Braid Monoids
Get PDF6 pages, 4 figuresBirman, Ko and Lee have introduced a new monoid --with an explicit presentation--whose group of fractions is the -strand braid group . Building on a new approach by Digne, Michel and himself, Bessis has defined a {\it dual} braid monoid for every finite Coxeter type Artin-Tits group extending the type A case. Here, we give an explicit presentation for this dual braid monoid in the case of types B and D, and we study the combinatorics of the underlying Garside structures
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