To some Hecke symmetries (i.e. Yang-Baxter braidings of Hecke type) we assign algebras called braided non-commutative spheres. For any such algebra, we introduce and compute a q-analog of the Chern-Connes index. Unlike the standard Chern-Connes index, ours is based on the so-called categorical trace specific for a braided category in which the algebra in question is represented. AMS Mathematics...

We give an overview of a new kind symmetry in physics which exists between observables and states and which is made possible by the language of Hopf algebras and quantum geometry. It has been proposed by the author as a feature of Planck scale physics. More recent work includes corresponding results at the semiclassical level of Poisson-Lie groups and at the level of braided groups and braided ...

We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory, embeddable quantum homogeneous spaces and braided group gauge theory, the latter being introduced now by these means. Examples include ones in which the gauge groups...

Braided Thompson’s groups are finitely presented groups introduced by Brin and Dehornoy which contain the ordinary braid groups Bn, the finitary braid group B∞ and Thompson’s group F as subgroups. We describe some of the metric properties of braided Thompson’s groups and give upper and lower bounds for word length in terms of the number of strands and the number of crossings in the diagrams use...

The main purpose of this paper is to study some relevant applications of the results on bialgebras of type one obtained in [AM1] in the framework of abelian braided monoidal categories. Let H be a braided bialgebra in a cocomplete and complete abelian braided monoidal category (M, c) satisfying AB5. Assume that the tensor product commutes with direct sums and is twosided exact. Let M be in HM H...

3D braided composite joints are the important components in CFRP truss, which have significant influence on the reliability and lightweight of structures. To investigate the mechanical performance of 3D braided composite joints, a numerical method based on the microscopic mechanics is put forward, the modeling technologies, including the material constants selection, element type, grid size, an...

This paper presents network coding based reliable disjoint and braided multipath routing (NC-RMR ) for sensor networks, which forms multipath by hop-by-hop method and only maintains local path information of each node without establishing end-to-end paths. Neighbors of each local node are divided into groups according to their hops to sink nodes to improve the network load balancing. For furthe...

We give an overview of a new kind symmetry in physics which exists between observables and states and which is made possible by the language of Hopf algebras and quantum geometry. It has been proposed by the author as a feature of Planck scale physics. More recent work includes corresponding results at the semiclassical level of Poisson-Lie groups and at the level of braided groups and braided ...

The notion of the genus of a quadratic form is generalized to vertex operator algebras. We define it as the modular braided tensor category associated to a suitable vertex operator algebra together with the central charge. Statements similar as known for quadratic forms are formulated. We further explain how extension problems for vertex operator algebras can be described in terms of the associ...

Based on the small parameter asymptotic homogenization theory, this article adopts the technology of digitized cell-based finite element method (DCB-FEM) to establish the digital cell-based mechanics analysis model of three-dimensional 4-directional braided composite material, analyzes and calculates the equivalent elasticity performance of 3D braided composite material using homogenization met...