We describe and study a four parameters deformation of the two products and the coproduct of the Hopf algebra of plane posets. We obtain a family of braided Hopf algebras, which are generically self-dual. We also prove that in a particular case (when the second parameter goes to zero and the first and third parameters are equal), this deformation is isomorphic, as a self-dual braided Hopf algeb...

We show that the nerve of a braided monoidal category carries a natural action of a simplicial E2-operad and is thus up to group completion a double loop space. Shifting up dimension twice associates to each braided monoidal category a 1-reduced lax 3-category whose nerve realizes an explicit double delooping whenever all cells are invertible. We deduce that lax 3-groupoids are algebraic models...

The notions of the crossed product and the braided category are discussed within the theory of C∗-algebras. Like in the purely algebraic approach of S. Majid these notions are used to generalize the quantum group theory. We give an example of a braided group. It coincides with the closed subset C = {z : |z| = . . . , q−2, q−1, 1, q, q2, . . . , 0} of the complex plane equipped with the q2braidi...

abstract morphological river models are designed to provide physical insight into the morphological response and to assist river engineers and managers in the design, operation and maintenance of river systems. here deterministic modeling weak for a dynamic and stochastic of nature river environment. specially, these could not predict the exact shape of the river bed, specially e.g. for braided...

Repair success for injuries to the flexor tendon in the hand is often limited by the in vivo behaviour of the suture used for repair. Common problems associated with the choice of suture material include increased risk of infection, foreign body reactions, and inappropriate mechanical responses, particularly decreases in mechanical properties over time. Improved suture materials are therefore n...

We establish braided tensor equivalences among module categories over the twisted quantum double of a finite group defined by an extension of a group G by an abelian group, with 3-cocycle inflated from a 3-cocycle on G. We also prove that the canonical ribbon structure of the module category of any twisted quantum double of a finite group is preserved by braided tensor equivalences. We give two...

After recalling the definition of a bicoalgebroid, we define comodules and modules over a bicoalgebroid. We construct the monoidal category of comodules, and define Yetter–Drinfel’d modules over a bicoalgebroid. It is proved that the Yetter–Drinfel’d category is monoidal and pre–braided just as in the case of bialgebroids, and is embedded into the one–sided center of the comodule category. We p...

Hughes defined a class of groups that act as local similarities on compact ultrametric spaces. Guba and Sapir had previously defined braided diagram groups over semigroup presentations. The two classes of groups share some common characteristics: both act properly by isometries on CAT(0) cubical complexes, and certain groups in both classes have type F∞, for instance. Here we clarify the relati...

We introduce the concept of pseudotwistor (with particular cases called twistor and braided twistor) for an algebra (A,μ, u) in a monoidal category, as a morphism T : A⊗ A → A ⊗ A satisfying a list of axioms ensuring that (A,μ ◦ T, u) is also an algebra in the category. This concept provides a unifying framework for various deformed (or twisted) algebras from the literature, such as twisted ten...