Related papers: Equations in Burnside groups
Consider a one-ended word-hyperbolic group. If it is the fundamental group of a graph of free groups with cyclic edge groups then either it is the fundamental group of a surface or it contains a finitely generated one-ended subgroup of…
We study the restriction of representations of Cayley-Hamilton algebras to subalgebras. This theory is applied to determine tensor products and branching rules for representations of quantum groups at roots of 1.
We study co-ideals in the core Hopf algebra underlying a quantum field theory.
A geometric characterization of the structure of the group of automorphisms of an arbitrary Birkhoff-Grothendieck bundle splitting $\bigoplus_{i=1}^{r} \mathcal(m_{i})$ over $\mathbb{C}\mathbb{P}^{1}$ is provided, in terms of its action on…
In this paper we define and study the algebraic conterpart of sovereign monoidal categories : cosovereign Hopf algebras.
Known and new results on free Boolean topological groups are collected. An account of properties which these groups share with free or free Abelian topological groups and properties specific of free Boolean groups is given. Special emphasis…
This paper is a companion article to the review paper by the present author devoted to the classification of matter constituents (chemical elements and particles) and published in the first part of the proceedings of The Second Harry Wiener…
We give a complete characterization of torsion-free hyperbolic groups which are homogeneous in the sense of first-order logic, in terms of the JSJ decompositions of their free factors.
In this work we investigate tensor completions of groups by associative rings, which were introduced by R.Lyndon and G.Baumslag in 1960s. The main result states that there exists an algorithm that decides if a given finite system of…
In this paper, we introduce and investigate \emph{bisemialgebras}and\emph{\ Hopf semialgebras} over commutative semirings. We generalize to the semialgebraic context several results on bialgebras and Hopf algebras over rings including the…
Hopf representation is a module and comodule with a consistency condition that is more general than the consistency condition of Hopf modules. For a Hopf algebra $H$, we construct an induced Hopf representation from a representation of a…
The group ring of the automorphism group of a p-group is studied using the automorphism groups of subgroups and quotient groups of P.
We give an elementary construction of polyhedra whose links are connected bipartite graphs, which are not necessarily isomorphic pairwise. We show, that the fundamental groups of some of our polyhedra contain surface groups. In particular,…
We continue our study of the quantum optics of a single photon interacting with a system of two level atoms. In this work we investigate the case of a periodic arrangement of atoms. We provide a general structure theorem characterizing the…
This paper surveys recent results on classifying partially hyperbolic diffeomorphisms. This includes the construction of branching foliations and leaf conjugacies on three-dimensional manifolds with solvable fundamental group.…
We find a finite free resolution of the counit of the free unitary quantum groups of van Daele and Wang and, more generally, Bichon's universal cosovereign Hopf algebras with a generic parameter matrix. This allows us to compute Hochschild…
We study the properties of geodesic currents on free groups, particularly the "intersection form" that is similar to Bonahon's notion of the intersection number between geodesic currents on hyperbolic surfaces.
In this paper we analyze a generic dynamical system with $\mathbb{D}_2$ constructed via a Cayley graph. We study the Hopf bifurcation and find conditions for obtaining a unique branch of periodic solutions. Our main result comes from…
This paper is concerned with the existence of periodic orbits on energy hypersurfaces in cotangent bundles of Riemannian manifolds defined by mechanical Hamiltonians. In \cite{bpv} it was proved that, provided certain geometric assumptions…
We give a new solution of the "homotopy periods" problem, as highlighted by Sullivan, which places explicit geometrically meaningful formulae first dating back to Whitehead in the context of Quillen's formalism for rational homotopy theory…