相关论文: Quantum torsors and Hopf-Galois objects

By using the language of cogroupoids, we show that Hopf-Galois objects of a twisted Calabi-Yau Hopf algebra with bijective antipode are still twisted Calabi-Yau, and give their Nakayama automorphism explicitly. As applications, cleft Galois…

We realize every closed flat 3-manifold as a cusp section of a complete, finite-volume hyperbolic 4-manifold whose symmetry group acts transitively on the set of cusps. Moreover, for every such 3-manifold, a dense subset of its flat metrics…

In this article, we construct an orbifold quantum cohomology twisted by a flat gerbe. Then we compute these invariants in the case of a smooth manifold and a discrete torsion on a global quotient orbifold.

The cusp was recently shown to admit the structure of a quantum homogeneous space, that is, its coordinate ring $B$ can be embedded as a right coideal subalgebra into a Hopf algebra $A$ such that $A$ is faithfully flat as a $B$-module. In…

We describe a locally trivial quantum principal U(1)-bundle over the quantum space S^2_{pq} which is a noncommutative analogue of the usual Hopf bundle. We also provide results concerning the structure of its total space algebra…

Let H be a cocommutative faithfully flat Hopf quasigroup in a strict symmetric monoidal category with equalizers. In this paper we introduce the notion of (strong) Galois H-object and we prove that the set of isomorphism classes of (strong)…

Starting from a Hopf algebra endowed with an action of a group G by Hopf automorphisms, we construct (by a twisted double method) a quasitriangular Hopf G-coalgebra. This method allows us to obtain non-trivial examples of quasitriangular…

We describe a universal factorization for a functor with values in finite-dimensional measured algebras. More precisely we contruct the quantum automorphism group of this functor. This general recontruction result allows us to recapture a…

We discuss quantum deformation of the affine transformation algebra. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators.

We prove that every quasitoric manifold admits an invariant metric of positive scalar curvature.

As is known to all, Hopf-Galois objects have a significant research value for analyzing tensor categories of comodules and classification questions of pointed Hopf algebras, and are natural generalizations of Hopf algebras with a…

Given a group $G$ with bounded torsion that acts properly on a systolic complex, we show that every solvable subgroup of $G$ is finitely generated and virtually abelian of rank at most $2$. In particular this gives a new proof of the above…

A universal R--matrix for the quantum Heisenberg algebra h(1)q is presented. Despite of the non--quasitriangularity of this Hopf algebra, the quantum group induced from it coincides with the quasitriangular deformation already known.

We give a notion of a comatrix coring which embodies all former constructions and, what is more interesting, leads to the formulation of a notion of Galois coring and the statement of a Faithfully Flat Descent Theorem that generalize the…

The question of whether or not a Hopf algebra $H$ is faithfully flat over a Hopf subalgebra $A$ has received positive answers in several particular cases: when $H$ (or more generally, just $A$) is commutative, or cocommutative, or pointed,…

Torsors under affine groups are generalized in the super context by super-torsors under affine super-groups. We investigate those super-torsors by using Hopf-algebra language and techniques. It is explicitly shown, under suitable…

We construct the join of noncommutative Galois objects (quantum torsors) over a Hopf algebra H. To ensure that the join algebra enjoys the natural (diagonal) coaction of H, we braid the tensor product of the Galois objects. Then we show…

It has been shown by J.Funk, P.Hofstra and B.Steinberg that any Grothendieck topos T is endowed with a canonical group object, called its isotropy group, which acts functorially on every object of T. We show that this group is in fact the…

We consider a quantum particle constrained to a curved layer of a constant width built over an infinite smooth surface. We suppose that the latter is a locally deformed plane and that the layer has the hard-wall boundary. Under this…

We describe Hopf-Galois objects over bicrossed product Hopf algebras. More precisely, we show that any right Hopf-Galois object over a bicrossed product of Hopf algebras is obtained from Hopf-Galois objects over the two factors and a…