We show that any pointed Hopf algebra with infinitesimal braiding associated to the conjugacy class of π ∈ Sn is infinitedimensional, if either the order of π is odd, or π is a product of disjoint cycles of odd order except for exactly two transpositions.

The Faddeev-Reshetikhin-Takhtajan method to construct matrix bialgebras from non-singular solutions of the quantum Yang-Baxter equation is extended to the anyonic or Z Z n-graded case. The resulting anyonic quantum matrices are braided groups in which the braiding is given by a phase factor.

By definition, a bialgebra H in a braided monoidal category (C, τ) is an algebra and coalgebra whose multiplication and comultiplication (and unit and counit) are compatible; the compatibility condition involves the braiding τ . The present paper is based upon the following simple observation: If H is a Hopf algebra, that is, if an antipode exists, then the compatibility condition of a bialgebr...

The non-Hermitian skin effect, as a unique feature of systems, will break the topological energy braiding Bloch bands in open boundary systems. Going beyond band theory, we unveil non-Bloch by introducing one-dimensional tight-binding model. We find generic class such Hopf link, which is generally generated effect. topologically robust against any perturbations without gap closing. Furthermore,...

Mechanical properties of hybrid braided composite rebars are evaluated and compared to theoretical predictions which account for specific processing parameters including yarn size, braiding machine setup, and fiber type. Using a combination of high modulus carbon (Thornel P-55S) and aramid (Kevlar 49) fibers bars have been produced of up to 10 mm diameter with a Young's modulus of 200 GPa, a bi...

Full-thickness scalp necrosis secondary to hair weave placement is a rare but serious complication of a common hairstyle. The defects can be large and may necessitate complex reconstruction with hair-bearing tissue. We report on the case of a young woman with extensive scalp loss following tight spiral braiding. The case description illustrates this relatively unknown complication, its treatmen...

We use the new approach of braiding sequences to prove exponential upper bounds for the number of Vassiliev invariants on knots with bounded braid index, bounded bridge number and arborescent knots. We prove, that any Vassiliev invariant of degree k is determined by its values on knots with braid index at most k+1.

We remove the need to physically transport computational anyons around each other from the implementation of computational gates in topological quantum computing. By using an anyonic analog of quantum state teleportation, we show how the braiding transformations used to generate computational gates may be produced through a series of topological charge measurements.