We find a new braided Hopf structure for the algebra satisfied by the entries of the braided matrix BSLq(2). A new nonbraided algebra whose coalgebra structure is the same as the braided one is found to be a two parameter deformed algebra. It is found that this algebra is not a comodule algebra under adjoint coaction. However, it is shown that for a certain value of one of the deformation param...

River systems in remote environments are often challenging to monitor and understand where traditional gauging apparatus are difficult to install or where safety concerns prohibit field measurements. In such cases, remote sensing, especially terrestrial time-lapse imaging platforms, offer a means to better understand these fluvial systems. One such environment is found at the proglacial Isortoq...

We obtain the double factorization of braided bialgebras or braided Hopf algebras, give relation among integrals and semisimplicity of braided Hopf algebra and its factors. We find an example which show that the 8th Kaplansky’s conjecture does not hold for braided Hopf algebras.

We introduce the notion of a braided Lie algebra consisting of a finite-dimensional vector space L equipped with a bracket [ , ] : L⊗L → L and a Yang-Baxter operator Ψ : L⊗L → L⊗L obeying some axioms. We show that such an object has an enveloping braided-bialgebra U(L). We show that every generic R-matrix leads to such a braided Lie algebra with [ , ] given by structure constants cK determined ...

Braided groups and braided matrices are novel algebraic structures living in braided or quasitensor categories. As such they are a generalization of super-groups and super-matrices to the case of braid statistics. Here we construct braided group versions of the standard quantum groups Uq(g). They have the same FRT generators l± but a matrix braided-coproduct ∆L = L⊗L where L = l+Sl−, and are se...

According to the Water Framework Directive (WFD), "good ecological status" of all aquatic environments should be achieved by 2015. To validate this objective, we set up management tools to assess the physical condition of rivers. To avoid field work, which is a long and tedious work, and in order to achieve homogeneous data throughout the network, we created geomatic tools based on an object-or...

We present a systematic introduction to the geometry of linear braided spaces. These are versions of R n in which the coordinates x i have braid-statistics described by an R-matrix. From this starting point we survey the author's braided-approach to q-deformation: braided differentiation, exponentials, Gaussians, integration and forms, i.e. the basic ingredients for q-deformed physics are cover...

This is a systematic introduction for physicists to the theory of algebras and groups with braid statistics, as developed over the last three years by the author. There are braided lines, braided planes, braided matrices and braided groups all in analogy with superlines, superplanes etc. The main idea is that the bose-fermi ±1 statistics between Grassmannn coordinates is now replaced by a gener...

The goal of this paper is to characterise certain probability laws on a class of quantum groups or braided groups that we will call nilpotent. First we introduce a braided analogue of the Heisenberg-Weyl group, which shall serve as standard example. We introduce Gaussian functionals on quantum groups or braided groups as functionals that satisfy an analogue of the Bernstein property, i.e. that ...

We show that the Witt class of a weakly group-theoretical non-degenerate braided fusion category belongs to the subgroup generated by classes of non-degenerate pointed braided fusion categories and Ising braided categories. This applies in particular to solvable nondegenerate braided fusion categories. We also give some sufficient conditions for a braided fusion category to be weakly group-theo...