Related papers: Ring-shaped exact Hopf solitons
Homogeneous compatible almost complex structures on symplectic manifolds are studied, focusing on those which are special, meaning that their Chern-Ricci form is a multiple of the symplectic form. Non Chern-Ricci flat ones are proven to be…
We present an overview of the notions of exact sequences of Hopf algebras and tensor categories and their connections. We also present some examples illustrating their main features; these include simple fusion categories and a natural…
We consider four dimensional conformally flat homogeneous pseudo Riemannian manifolds. According to forms (Seger types) of the Ricci operator, we provide a full classification of four dimensional pseudo Riemannian conformally flat…
Among closed G2-structures there are two very distinguished classes: Laplacian solitons and Extremally Ricci-pinched G2-structures. We study the existence problem and explore possible interplays between these concepts in the context of…
3D topological solitons are marvels of mathematical physics that arise in theoretical models in elementary particle and nuclear physics, condensed matter, and cosmology. A particularly interesting type of them is described by the…
This work provides the first experimental elucidation of quantum topological effects in individual hopfions, establishing their potential as building blocks for three-dimensional topological quantum spintronics. The observed Non-Abelian…
We prove the existence of lattice isomorphic line arrangements having $\pi_1$-equivalent or homotopy-equivalent complements and non homeomorphic embeddings in the complex projective plane. We also provide two explicit examples, one is…
We describe rings over which every right module is almost injective. We give a description of rings over which every simple module is a almost projective.
We study affine Jacobi structures on an affine bundle $\pi:A\to M$, i.e. Jacobi brackets that close on affine functions. We prove that there is a one-to-one correspondence between affine Jacobi structures on $A$ and Lie algebroid structures…
We show that the direct sum of the cohomology groups of the alternating subgroups of the family of Coxeter groups of Type B exhibits an almost-Hopf ring structure. We apply techniques developed by Giusti and Sinha to fully compute a…
The modular group algebra of an elementary abelian p-group is isomorphic to the restricted enveloping algebra of commutative restricted Lie algebra. The different ways of regarding this algebra result in different Hopf algebra structures…
Motivated by physics, we propose two conjectures regarding the cohomology ring of the crepant resolutions of orbifolds and cohomological invariants of K-equivalent manifolds.
Let G be an exceptional Lie group with a maximal torus T. Based on common properties in the Schubert presentation of the cohomology ring H*(G/T;F_{p}) DZ1, and concrete expressions of generalized Weyl invariants for G over F_{p}, we obtain…
The article is devoted to microbundles over topological rings. Their structure, homomorphisms, automorphisms and extensions are studied. Moreover, compactifications and inverse spectra of microbundles over topological rings are…
We present a direct connection between torus knots and Hopfions by finding stable and static solutions of the extended Faddeev-Skyrme model with a ferromagnetic potential term. (P,Q)--torus knots consisting of |Q| sine-Gordon kink strings…
In the present note we discuss two different ring structures on the set of holomorphic discrete series of a causal symmetric space of Cayley type $G/H$ and we suggest a new interpretation of Rankin-Cohen brackets in terms of intertwining…
In this note, we present a construction method and an explicit example of nongradient (expanding or indefinite) Ricci almost soliton in a warped product. Moreover, we show a rigidity result for the Gaussian soliton.
The dynamical model on 3+1 dimensional spacetime admitting soliton solutions is discussed. The proposal soliton is localized in the vicinity of a closed contour, which could be linked and/or knotted. The topological charge is Hopf…
Magnetic hopfions are string-like three-dimensional topological solitons, characterised by the Hopf invariant. They serve as a fundamental prototype for three-dimensional magnetic quasi-particles and are an inspiration for novel device…
We derive necessary and sufficient conditions for an ambiskew polynomial ring to have a Hopf algebra structure of a certain type. This construction generalizes many known Hopf algebras, for example U(sl2), U_q(sl2) and the enveloping…