this paper is devoted to study of a partial differential equation governing panel motion in supersonic flow. this pde can be transformed to an ode by means of a galerkin method. here by using a criterion which is closely related to the routh-hurwitz criterion, we investigate the mentioned transformed ode from hopf bifurcation point of view. in fact we obtain a region for existence of simple hop...

Let G be any group and let K(G) denote the multiplier Hopf algebra of complex functions with finite support in G. The product in K(G) is pointwise. The comultiplication on K(G) is defined with values in the multiplier algebra M(K(G)⊗K(G)) by the formula (∆(f))(p, q) = f(pq) for all f ∈ K(G) and p, q ∈ G. In this paper we consider multiplier Hopf algebras B (over C) such that there is an embeddi...

Let H be a finite dimensional non-semisimple Hopf algebra over an algebraically closed field k of characteristic 0. If H has no nontrivial skew-primitive elements, we find some bounds for the dimension of H 1 , the second term in the coradical filtration of H. Using these results, we are able to show that every Hopf algebra of dimension 14 is semisimple and thus isomorphic to a group algebra or...

Let L be a Galois extension of K, fields, with Galois group Γ. We obtain two results. First, if Γ = Hol(Zpe ), we determine the number of Hopf Galois structures on L/K where the associated group of the Hopf algebra H is Γ (i.e. L⊗K H ∼= L[Γ]). Now let p be a safeprime, that is, p is a prime such that q = (p−1)/2 > 2 is also prime. If L/K is Galois with group Γ = Hol(Zp), p a safeprime, then for...

Let X = GM be a finite group factorisation. It is shown that the quantum double D(H) of the associated bicrossproduct Hopf algebra H = kM⊲◭k(G) is itself a bicrossproduct kX⊲◭k(Y ) associated to a group Y X, where Y = G×Mop. This provides a class of bicrossproduct Hopf algebras which are quasitriangular. We also construct a subgroup Y X associated to every order-reversing automorphism θ of X. T...

A strict 2-group is a 2-category with one object in which all morphisms and all 2morphisms have inverses. 2-Groups have been studied in the context of homotopy theory, higher gauge theory and Topological Quantum Field Theory (TQFT). In the present article, we develop the notions of trialgebra and cotrialgebra, generalizations of Hopf algebras with two multiplications and one comultiplication or...

A strict 2-group is a 2-category with one object in which all morphisms and all 2morphisms have inverses. 2-Groups have been studied in the context of homotopy theory, higher gauge theory and Topological Quantum Field Theory (TQFT). In the present article, we develop the notions of trialgebra and cotrialgebra, generalizations of Hopf algebras with two multiplications and one comultiplication or...

This paper provides a primer in quantum field theory (QFT) based on Hopf algebra and describes new Hopf algebraic constructions inspired by QFT concepts. The following QFT concepts are introduced: chronological products, S-matrix, Feynman diagrams, connected diagrams, Green functions, renormalization. The use of Hopf algebra for their definition allows for simple recursive derivations and lead ...

We prove that a depth two Hopf subalgebra K of a semisimple Hopf algebra H is normal (where the ground field k is algebraically closed of characteristic zero). This means on the one hand that a Hopf subalgebra is normal when inducing (then restricting) modules several times as opposed to one time creates no new simple constituents. This point of view was taken in the paper [13] which establishe...

Quantum duality principle is applied to study classical limits of quantum algebras and groups. For a certain type of Hopf algebras the explicit procedure to construct both classical limits is presented. The canonical forms of quantized Lie-bialgebras are proved to be two-parametric varieties with two classical limits called dual. When considered from the point of view of quantized symmetries su...