Related papers: Coset for Hopf fibration and Squashing
Following work by the first author and Banchoff, we investigate triangulations of real and complex projective spaces of real and complex dimension $k$ that are adapted to the decomposition into "zones of influence" around the points…
We present various improvements to the deformation method for computing the zeta function of smooth projective hypersurfaces over finite fields using $p$-adic cohomology. This includes new bounds for the $p$-adic and $t$-adic precisions…
We present a generalization to 3-qubits of the standard Bloch sphere representation for a single qubit and of the 7-dimensional sphere representation for 2 qubits presented in Mosseri {\it et al.}\cite{Mosseri2001}. The Hilbert space of the…
Recollect that Heron's formula for the area of a triangle given its sides has a counterpart given the medians instead, which carries an extra factor of $\frac{4}{3}$. On the one hand, we formulate the pair of these in Linear Algebra terms,…
We show that certain twisting deformations of a family of supersolvable groups are simple as Hopf algebras. These groups are direct products of two generalized dihedral groups. Examples of this construction arise in dimensions 60 and…
A fibration of ${\mathbb R}^n$ by oriented copies of ${\mathbb R}^p$ is called skew if no two fibers intersect nor contain parallel directions. Conditions on $p$ and $n$ for the existence of such a fibration were given by Ovsienko and…
The main application of Heavy Quark Effective Theory (HQET) and of Soft Collinear Effective Theory (SCET) is in establishing factorization theorems for exclusive and semi-inclusive decays of heavy mesons. However, the calculation of the…
We introduce $q$-deformed connections on the quantum 2-sphere and 3-sphere, satisfying a twisted Leibniz rule in analogy with $q$-deformed derivations. We show that such connections always exist on projective modules. Furthermore, a…
We show that all finite dimensional pointed Hopf algebras with the same diagram in the classification scheme of Andruskiewitsch and Schneider are cocycle deformations of each other. This is done by giving first a suitable characterization…
In this paper, we present a Hopf algebra description of a bosonic quantum model, using the elementary combinatorial elements of Bell and Stirling numbers. Our objective in doing this is as follows. Recent studies have revealed that…
We define certain deformations between minimal and non-minimal constant mean curvature (CMC) surfaces in Euclidean space $E^3$ which preserve the Hopf differential. We prove that, given a CMC $H$ surface $f$, either minimal or not, and a…
In this note, we collect various properties of Seifert homology spheres from the viewpoint of Dehn surgery along a Seifert fiber. We expect that many of these are known to various experts, but include them in one place which we hope to be…
The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash…
In a recent paper (1994 {\sl J.\ Phys.\ A: Math.\ Gen.\ }{\bf 27} 5907), Oh and Singh determined a Hopf structure for a generalized $q$-oscillator algebra. We prove that under some general assumptions, the latter is, apart from some…
We define in the setting of homotopy type theory an H-space structure on $\mathbb S^3$. Hence we obtain a description of the quaternionic Hopf fibration $\mathbb S^3\hookrightarrow\mathbb S^7\twoheadrightarrow\mathbb S^4$, using only…
This paper together with the previous one (arXiv:hep-th/0604146) presents the detailed description of all quantum deformations of D=4 Lorentz algebra as Hopf algebra in terms of complex and real generators. We describe here in detail two…
In this talk I discuss a recently developed "Unfolded Quantization Framework". It allows to introduce a Hamiltonian Second Quantization based on a Hopf algebra endowed with a coproduct satisfying, for the Hamiltonian, the physical…
We show that all finite dimensional pointed Hopf algebras with the same diagram in the classification scheme of Andruskiewitsch and Schneider are cocycle deformations of each other. This is done by giving first a suitable characterization…
The Hopf fibration has inspired any number of geometric structures in physical systems, in particular in chiral liquid crystalline materials. Because the Hopf fibration lives on the three sphere, $\mathbb{S}^3$, some method of projection or…
We formulate the Hopf algebra underlying the su(2|2) worldsheet S-matrix of the AdS_5 x S^5 string in the AdS/CFT correspondence. For this we extend the previous construction in the su(1|2) subsector due to Janik to the full algebra by…