Related papers: Reductions related with Hopf maps

This work seeks to make explicit the operational connection between the preparation of two-level quantum systems with their corresponding description (as states) in a Hilbert space. This may sound outdated, but we show there is more to this…

This sequel to Derived Langlands II studies some PSH algebras and their numerical invariants, which generalise the epsilon factors of the local Langlands Programme. It also describes a conjectural Hopf algebra structure on the sum of the…

With the help of a new type of functionals we study manifolds diffeomorphic to $S^2\times S^2$ and establish, in particular, the Hopf conjecture.

We employ the recently discovered Hopf algebra structure underlying perturbative Quantum Field Theory to derive iterated integral representations for Feynman diagrams. We give two applications: to massless Yukawa theory and quantum…

We provide a simple derivation of metrics for fundamental geometrical deformations such as Hopf fibration, squashing and Z_k quotient which play essential roles in recent studies on the AdS4/CFT3. A general metric formula of Hopf fibrations…

Using the shuffle structure of the graphs, we introduce a new kind of the Hopf algebraic structure for tagged graphs with, or without loops. Like a quantum group structure, its product is non-commutative. With the help of the Hopf algebraic…

A Hopf texture is a vacuum field configuration of isovector fields which is an onto map from the space as a large three sphere to the vacuum manifold $S^2$. We construct a Hopf texture with spherically symmetric energy density and discuss…

Using motivic homotopy theory we produce several explicit polynomial representatives of the suspension of the Hopf map defined over the integers. We derive from this computation an explicit rank 2 vector bundle on the Jouanolou device of…

Rational Hopf algebras (certain quasitriangular weak quasi-Hopf $^*$-algebras) are expected to describe the quantum symmetry of rational field theories. In this paper methods are developped which allow for a classification of all rational…

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for…

We introduce Hopf images of coactions of Hopf algebras and develop their role in the geometry of quantum principal bundles. Assuming cosemisimplicity of the structure Hopf algebra, we show that every quantum principal bundle equipped with a…

We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of transverse index theory for foliations.

In the recent years, Hopf algebras have been introduced to describe certain combinatorial properties of quantum field theories. I will give a basic introduction to these algebras and review some occurrences in particle physics.

This is an innovative treatise on triangles, resting upon 1) 3-body problem techniques including mass-weighted relative Jacobi coordinates. 2) Part I's detailed layer-by-layer topological and geometrical study of Kendall-type shape spaces -…

We reformulate the method recently proposed for constructing quasitriangular Hopf algebras of the quantum-double type from the R-matrices obeying the Yang-Baxter equations. Underlying algebraic structures of the method are elucidated and an…

For our own education, we reconstruct the Hopf algebra of Connes and Moscovici obtained by the action of vector fields on a crossed product of functions by diffeomorphisms. We extend the realization of that Hopf algebra in terms of rooted…

We construct a Hopf algebra structure on the space of specified Feynman graphs of a quantum field theory. We introduce a convolution product and a semigroup of characters of this Hopf algebra with values in some suitable commutative algebra…

In this paper we contribute to the classification of Hopf algebras of dimension pq, where p,q are distinct prime numbers. More precisely, we prove that if p and q are odd primes with p<q<2p+3, then any complex Hopf algebra of dimension pq…

The Hopf index, a topological invariant that quantifies the linking of preimage fibers, is fundamental to the structure and stability of hopfions. In this work, we propose a new mathematical framework for modeling hopfions with high Hopf…

Given any smooth fibration of the unit 3-sphere by great circles, we show that the distribution of 2-planes orthogonal to the great circle fibres is a tight contact structure, a fact well known in the special case of the Hopf fibrations.…