Related papers: A simplicial model for the Hopf map

Let X be a locally compact space with a continuous proper action of a locally compact group G. Assuming that X satisfies a certain kind of duality in equivariant bivariant Kasparov theory, we can enrich the classical construction of…

The purpose of this article is to define the topological realization of a simplicial presheaf and to prove (under appropriate conditions) that it is homotopy-invariant under Illusie weak equivalence. In particular this applies to the site…

We introduce and study a class of Hopf algebras $H(G, \chi, \eta, b, c, \beta)$ which are two-step Ore extensions of a group algebra $\mathbb{K}[G]$. This construction unifies and generalizes some known families of Hopf algebras such as…

We show that the maximal extension sl(2) times psl(2|2) times C3 of the sl(2|2) superalgebra can be obtained as a contraction limit of the semi-simple superalgebra d(2,1;epsilon) times sl(2). We reproduce earlier results on the…

We consider a generalisation of the Majid's mirror product of a Hopf algebra H, when one of the components of the product is replaced by a twist. This leads to a new "twisted mirror product" construction for cocycle bicrossproduct Hopf…

We construct explicit examples of weak Hopf algebras (actually face algebras in the sense of Hayashi) via vacant double groupoids as explained in \http://arxiv.org/abs/math.QA/0308228. To this end, we first study the Kac exact sequence for…

This paper provides a primer in quantum field theory (QFT) based on Hopf algebra and describes new Hopf algebraic constructions inspired by QFT concepts. The following QFT concepts are introduced: chronological products, S-matrix, Feynman…

The Leigh-Strassler family of N=1 marginal deformations of the N=4 SYM theory admits a Hopf algebra symmetry which is a quantum group deformation of the SU(3) part of the R-symmetry of the Ncal=4 theory. We investigate how this quantum…

We construct a coherent Hopf 2-algebra in terms of Hopf coquasigroups, which relax the coassociativity condition and generalize the results in \cite{XH2023}. We also study quasi coassociative Hopf coquasigroups, and show that they give rise…

Let a torus $T$ act on a symplectic manifold $(M,\omega)$ with moment map $\phi$. We say that the Hamiltonian $T$-manifold $(M,\omega,\phi)$ has complexity one if $\frac{1}{2} \dim M - \dim T = 1$, and that it is K\"ahler if it admits an…

We construct cup products of two different kinds for Hopf-cyclic cohomology. When the Hopf algebra reduces to the ground field our first cup product reduces to Connes' cup product in ordinary cyclic cohomology. The second cup product…

For a given spectral curve, we construct a family of symplectic dual spectral curves for which we prove an explicit formula expressing the $n$-point functions produced by the topological recursion on these curves via the $n$-point functions…

We study the topology of the space of harmonic maps from $S^2$ to \CP 2$. We prove that the subspaces consisting of maps of a fixed degree and energy are path connected. By a result of Guest and Ohnita it follows that the same is true for…

We present contraction prescription of the quantum groups: from $SU_q(2)$ to $E_{\kappa}(2)$. Our strategy is different then one chosen in ref. [P. Zaugg, J. Phys. A {\bf 28} (1995) 2589]. We provide explicite prescription for contraction…

We introduce the notion of an effective Kan fibration, a new mathematical structure that can be used to study simplicial homotopy theory. Our main motivation is to make simplicial homotopy theory suitable for homotopy type theory. Effective…

Let $(H, \sigma)$ be a coquasitriangular Hopf algebra, not necessarily finite dimensional. Following methods of Doi and Takeuchi, which parallel the constructions of Radford in the case of finite dimensional quasitriangular Hopf algebras,…

To a marked simplicial set one can associate its path chain complex, and define its homology to be the homology of this complex, inspired by path homology theories for directed graphs, quivers, and marked categories. Given a marked…

We present two approaches to constructing an integration map for smooth Deligne cohomology. The first is defined in the simplicial model, where a class in Deligne cohomology is represented by a simplicial form, and the second in a related…

A simplicial complement P is a sequence of subsets of [m] and the simplicial complement P corresponds to a unique simplicial complex K with vertices in [m]. In this paper, we defined the homology of a simplicial complement…

Let $\mathcal{C}$ be a decomposable plane curve over an algebraically closed field $k$ of characteristic 0. That is, $\mathcal{C}$ is defined in $k^2$ by an equation of the form $g(x) = f(y)$, where $g$ and $f$ are polynomials of degree at…