Related papers: On Biproducts and Extensions

Additive deformations of bialgebras in the sense of Wirth are deformations of the multiplication map of the bialgebra fulfilling a compatibility condition with the coalgebra structure and a continuity condition. Two problems concerning…

The Hopf order of an element $h$ of a Hopf algebra $H$ is the least $n$ such that the $n$-th Hopf power of $h$ is trivial. For some bismash product Hopf algebras obtained from factorizable groups (including Drinfeld doubles of some groups)…

We derive necessary and sufficient conditions for an Ore extension of a Hopf algebra to have a Hopf algebra structure of a certain type. This construction generalizes the notion of Hopf-Ore extension, called a generalized Hopf-Ore…

We parameterize the finite-dimensional irreducible representations of a class of pointed Hopf algebras over an algebraically closed field of characteristic zero by dominant characters. The Hopf algebras we are considering arise in the work…

We introduce and study new families of finite-dimensional Hopf algebras with the Chevalley property that are not pointed nor semisimple arising as twistings of quantum linear spaces. These Hopf algebras generalize the examples introduced in…

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…

The quiver Hopf algebras are classified by means of ramification systems with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Hopf algebras of type one.

In this dissertation we study the coefficients spaces (SAYD modules) of Hopf-cyclic cohomology theory over a certain family of bicrossed product Hopf algebras, and we compute the Hopf-cyclic cohomology of such Hopf algebras with…

We describe certain quiver Hopf algebras by parameters. This leads to the classification of multiple Taft algebras as well as pointed Yetter-Drinfeld modules and their corresponding Nichols algebras. In particular, when the ground-field $k$…

An algebra extension A | B is right depth two if its tensor-square A\otimes_B A is in the Dress category Add A as A-B-bimodules. We consider necessary conditions for right, similarly left, D2 extensions in terms of partial A-invariance of…

We carry on the investigation initiated in [15] : we describe new shuffle products coming from some special functions and group them, along with other products encountered in the literature, in a class of products, which we name…

We extend the theory of Interacting Hopf algebras with an order primitive, and give a sound and complete axiomatisation of the prop of polyhedral cones. Next, we axiomatise an affine extension and prove soundness and completeness for the…

Let H be a quasi-Hopf algebra, a weak Hopf algebra or a braided Hopf algebra. Let B be an H-bicomodule algebra such that there exists a morphism of H-bicomodule algebras v:H\rightarrow B. Then we can define an object B^{co(H)} which is a…

Let k be any field. We consider the Hopf-Schur group of k, defined as the subgroup of the Brauer group of k consisting of classes that may be represented by homomorphic images of Hopf algebras over k. We show here that twisted group…

We study the representations of two types of pointed Hopf algebras: restricted two-parameter quantum groups, and the Drinfel'd doubles of rank one pointed Hopf algebras of nilpotent type. We study, in particular, under what conditions a…

We describe extension classes arising in the $\ell$-adic and Hodge cohomology of Hilbert modular varieties, generalising results of Caspar to arbitrary dimensions. We show that this description is consistent with the "plectic conjectures"…

Hopf (bi-)modules and crossed modules over a bialgebra B in a braided monoidal category C are considered. The (braided) monoidal equivalence of both categories is proved provided B is a Hopf algebra (with invertible antipode). Bialgebra…

The Hopf envelope of a bialgebra is the free Hopf algebra generated by the given bialgebra. Its existence, as well as that of the cofree Hopf algebra, is a well-known fact in Hopf algebra theory, but their construction is not particularly…

Let $S$ be the left $R$-bialgebroid of a depth two extension with centralizer $R$ as defined in math.QA/0108067. We show that the left endomorphism ring of depth two extension, not necessarily balanced, is a left $S$-Galois extension of…

We study the Hopf structure of a class of dual operator algebras corresponding to certain semigroups. This class of algebras arises in dilation theory, and includes the noncommutative analytic Toeplitz algebra and the multiplier algebra of…