We give a different proof for a structure theorem of Hausser and Nill on Hopf modules over quasi-Hopf algebras. We extend the structure theorem to a classification of two-sided two-cosided Hopf modules by YetterDrinfeld modules, which can be defined in two rather different manners for the quasi-Hopf case. The category equivalence between Hopf modules and Yetter-Drinfeld modules leads to a new c...

We study holomorphic locally homogeneous geometric structures modelled on line bundles over the projective line. We classify these structures on primary Hopf surfaces. We write out the developing map and holonomy morphism of each of these structures explicitly on each primary Hopf surface.

The classical Clifford correspondence for normal subgroups is considered in the more general setting of semisimple Hopf algebras. We prove that this correspondence still holds if the extension determined by the normal Hopf subalgebra is cocentral.

We show that a semisimple Hopf algebra A is group theoretical if and only if its Drinfeld double is a twisting of the Dijkgraaf-Pasquier-Roche quasi-Hopf algebra D(Σ), for some finite group Σ and some ω ∈ Z(Σ, k×). We show that semisimple Hopf algebras obtained as bicrossed products from an exact factorization of a finite group Σ are group theoretical. We also describe their Drinfeld double as ...

We reformulate Kauffman’s method of defining invariants of 3-manifolds intrinsically in terms of right integrals on certain finite dimensional Hopf algebras and define a type of universal invariants of framed tangles and invariants of 3-manifolds.

James constructed a functorial homotopy decomposition ΣΩΣX ' W∞ n=1 ΣX (n) for path-connected, pointed CW -complexes X. We generalize this to a functorial decomposition of ΣA where A is any functorial retract of a looped co-H space. This is used to construct Hopf invariants in a more general context. As well, when A = ΩY is the loops on a co-H space, we show that the wedge summands of ΣΩY furth...

This paper is a companion to the Boardman–Wilson paper on the ring spectrum P (n). When the prime is 2, this spectrum is not commutative, which introduces several complications. Here, we supply the necessary details of the relevant Hopf algebroids and Hopf ring for this case.

Coalgebra-Galois extensions generalise Hopf-Galois extensions, which can be viewed as non-commutative torsors. In this paper it is analysed when a coalgebra-Galois extension is a separable, split, or strongly separable extension.

Abstract. This article attempts to analyze the Hopf bifurcation behavior of a railway wheelset in the presence of dead-zone and yaw damper nonlinearities. A model that is more precise than Yang and Ahmadian is investigated. Using Bogoliubov-Mitropolsky averaging method and critical speed, the amplitude of the limit cycle in the presence of the mentioned nonlinearities is taken into consideratio...