Related papers: On vector field generated by the Hopf map $S^3$ on…
The classical Hopf invariant is defined for a map f: S^r -> X. Here we define `hcat' which is some kind of Hopf invariant built with a construction in Ganea's style, valid for maps not only on spheres but more generally on a `relative…
This note presents a procedure of constructing a higher dimensional sphere map from a lower dimensional one and gives an explicit formula for smooth sphere map with a given degree. As an application a new proof of a generalized…
Join-preserving maps on the discrete time scale $\omega^+$, referred to as time warps, have been proposed as graded modalities that can be used to quantify the growth of information in the course of program execution. The set of time warps…
The objects of study in this paper are Hopf algebras $H$ which are finitely generated algebras over an algebraically closed field and are extensions of a commutative Hopf algebra by a finite dimensional Hopf algebra. Basic structural and…
We show that the space of orthogonally separable coordinates on the sphere $S^3$ induces a natural family of integrable systems, which after symplectic reduction leads to a family of integrable systems on $S^2 \times S^2$. The generic…
By the method of discrete transformation equations of 3-th wave hierarchy are constructed. The main difference compare with the systems connected with $A_1$ algebra consists in a fact that in $A_2$ case there are two different systems of…
A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum groups, we…
We introduce a general class of combinatorial objects, which we call \emph{multi-complexes}, which simultaneously generalizes graphs, multigraphs, hypergraphs and simplicial and delta complexes. We introduce a natural algebra of…
Some models providing shell-shaped static solutions with compact support (compactons) in 3+1 and 4+1 dimensions are introduced, and the corresponding exact solutions are calculated analytically. These solutions turn out to be topological…
We endow the space of rooted planar trees with an structure of Hopf algebra. We prove that variations of such a structure lead to Hopf algebras on the spaces of labelled trees, $n$--trees, increasing planar trees and sorted trees. These…
We present an explicit description of the Hopf 2-cocycles involved in the classification of finite dimensional pointed and copointed Hopf algebras over the symmetric group on three letters. We determine which cocycles are exponentials of…
Given a PDE in [10] it is proposed a method for constructing solutions by considering an associative real algebra A, and a suitable affine vector field ${\varphi}$ with respect to which the components of all the functions…
In a first part, we formalize the construction of combinatorial Hopf algebras from plactic-like monoids using polynomial realizations. Thank to this construction we reveal a lattice structure on those combinatorial Hopf algebras. As an…
A Hopf Galois structure on a finite field extension $L/K$ is a pair $(H,\mu)$, where $H$ is a finite cocommutative $K$-Hopf algebra and $\mu$ a Hopf action. In this paper we present a program written in the computational algebra system…
Exactly solvable models in quantum many body dynamics provide valuable insights into many interesting physical phenomena, and serve as platforms to rigorously investigate fundamental theoretical questions. Nevertheless, they are extremely…
The development of the theory of three-dimensional harmonic mappings is considered. The new classes of mappings that generate three-dimensional harmonic functions are introduced. The physical interpretation of these mappings is applied to…
Nonholonomic systems are variational models commonly used for mechanical systems with ideal no-slip constraints. This note provides a differential-geometric derivation of the nonholonomic equations of motion for an arbitrary rigid body…
It is shown that smooth maps $f: S^3 \rightarrow S^3$ contain two countable families of harmonic representatives in the homotopy classes of degree zero and one.
Separable Hamiltonian systems either in sphero-conical coordinates on a $S^2$ sphere or in elliptic coordinates on a ${\mathbb R}^2$ plane are described in an unified way. A back and forth route connecting these Liouville Type I separable…
Differential geometry of the quantum Lie superalgebra of the extended quantum superplane and its Z$_2$-graded Hopf algebra structure is obtained. Its Z$_2$-graded dual Hopf algebra is also given.