Related papers: Pointlike Hopf defects in Abelian projections

For rank-two $A$-motives defined over local fields with odd characteristic, we give an analogue of a theorem of Imai stating that abelian varieties with good reduction over $p$-adic fields have only finitely many torsion points values in…

We review the dual relationship between various compact U(1) lattice models and Abelian Higgs models, the latter being the disorder field theories of line-like topological excitations in the systems. We point out that the predicted…

This letter presents a novel model that characterizes the curvature of space-time, influenced by a massive gauge field in the early universe. This curvature can lead to a multitude of observations, including the Hubble tension issue and the…

Ten Abelian twist deformations of acceleration-enlarged Newton-Hooke Hopf algebra are considered. The corresponding quantum space-times are derived as well. It is demonstrate that their contraction limit $\tau \to \infty$ leads to the new…

We construct the vector space dual to the space of right-invariant differential forms construct from a first order differential calculus on inhomogeneous quantum group. We show that this vector space is equipped with a structure of a Hopf…

There are few known computable examples of non-abelian surface holonomy. In this paper, we give several examples whose structure 2-groups are covering 2-groups and show that the surface holonomies can be computed via a simple formula in…

In this paper, we study topological properties of 3D lattice dimer model. We demonstrate, that the dimer model on a bipartite lattice possesses topological defects, which are exactly characterized by Hopf invariant. We derive its explicit…

Motivated by newly discovered properties of instantons on non-compact spaces, we realised that certain analytic invariants of vector bundles detect fine geometric properties. We present numerical algorithms, implemented in Macaulay 2, to…

We show that semisimple Hopf algebras having a self-dual faithful irreducible comodule of dimension 2 are always obtained as abelian extensions with quotient Z_2. We prove that nontrivial Hopf algebras arising in this way can be regarded as…

We construct a new type of quantum invariant of closed framed $3$-manifolds with the vanishing first Betti number. The invariant is defined for any finite dimensional Hopf algebra, such as small quantum groups, and is based on ideal…

We determine finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero, whose Hopf coradical is isomorphic to a non-pointed basic Hopf algebra of dimension $24$ and the infinitesimal braidings are…

Let $(\mathfrak{g},[p])$ be a restricted Lie algebra over an algebraically closed field $k$ of characteristic $p\!\ge \!3$. Motivated by the behavior of geometric invariants of the so-called $(\mathfrak{g},[p])$-modules of constant $j$-rank…

We introduce the notion of $\pi^2$-graded Hopf algebra, where the grading is by the double groupoid of commutative diagrams of a finite groupoid $\pi$. The finite dimensional representations of a $\pi^2$-graded Hopf algebra form a rigid…

The variety of skew braces contains several interesting subcategories as subvarieties, as for instance the varieties of radical rings, of groups and of abelian groups. In this article the methods of non-abelian homological algebra are…

We study the Abelian projection of an instanton in $R^3 \times S^1$ as a function of temperature (T) and non-trivial holonomic twist ($\omega$) of the Polyakov loop at infinity. These parameters interpolate between the circular monopole…

The dual Meissner effect is described and numerically observed in a gauge-invariant way in lattice Monte-Carlo simulations of pure SU(2) QCD. A gauge-invariant Abelian-like field strength is defined in terms of a unit-vector in color space…

Associated to every connected, topological space $X$ there is a Hopf algebra - the Pontrjagin ring of the based loop space of the configuration space of two points in X. We prove that this Hopf algebra is not a homotopy invariant of the…

I give a brief summary of the results reported in hep-th 0306013 in collaboration with G. Amelino-Camelia and F. D'Andrea. I focus on the analysis of the symmetries of $\kappa$-Minkowski noncommutative space-time, described in terms of a…

The examples of solutions of the system of differential equations generated by the Hopf map $S^3\rightarrow S^2$ are constructed. Their properties are discussed.

Higher extensions and higher central extensions, which are of importance to non-abelian homological algebra, are studied, and some fundamental properties are proven. As an application, a direct proof of the invariance of the higher Hopf…