Related papers: Quantum Double for QuasiHopf Algebras

We generalise the quantum double construction of Drinfel'd to the case of the (Hopf) algebra of suitable functions on a compact or locally compact group. We will concentrate on the *-algebra structure of the quantum double. If the conjugacy…

In a previous paper the authors constructed a class of quasi-Hopf algebras $D^{\omega}(G, A)$ associated to a finite group $G$, generalizing the twisted quantum double construction. We gave necessary and sufficient conditions, cohomological…

In previous work the authors introduced a new class of modular quasi-Hopf algebras $D^{\omega}(G, A)$ associated to a finite group $G$, a central subgroup $A$, and a $3$-cocycle $\omega\in Z^3(G, C^x)$. In the present paper we propose a…

It is shown in math.QA/0310253 that a finite dimensional quasi-Hopf algebra over the complex numbers with radical of codimension 2 is twist equivalent to a Nichols Hopf algebra, or to a lifting of one of four special quasi-Hopf algebras of…

We construct quasi-Hopf algebras associated with a semisimple Lie algebra, a complex curve and a rational differential. This generalizes our previous joint work with V. Rubtsov (Israel J. Math. (1999) and q-alg/9608005).

We generalize the fundamental structure Theorem on Hopf (bi)-modules by Larson and Sweedler to quasi-Hopf algebras H. If H is finite dimensional this proves the existence and uniqueness (up to scalar multiples) of integrals in H. Among…

One way to obtain Quantized Universal Enveloping Algebras (QUEAs) of non-semisimple Lie algebras is by contracting QUEAs of semisimple Lie algebras. We prove that every contracted QUEA in a certain class is a cochain twist of the…

For a finite-dimensional Hopf algebra $H$, the canonical elements of the Heisenberg doubles $\mathcal{H}(H^\ast)$ and $\mathcal{H}(H)$ satisfy the pentagon and Hopf equations, respectively. In this paper we construct quasi-Hopf analogues of…

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products are constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are…

Let $H$ be a quasitriangular quasi-Hopf algebra, we construct a braided group $\underline{H}$ in the quasiassociative category of left $H$-modules. Conversely, given any braided group $B$ in this category, we construct a quasi-Hopf algebra…

In this paper, we present a general method for constructing finite-dimensional quasi-Hopf algebras from finite abelian groups and braided vector spaces of Cartan type. The study of such quasi-Hopf algebras leads to the classification of…

We introduce and investigate the basic properties of an involutory (dual) quasi-Hopf algebra. We also study the representations of an involutory quasi-Hopf algebra and prove that an involutory dual quasi-Hopf algebra with non-zero integral…

It is shown in math.QA/0301027 that a finite dimensional quasi-Hopf algebra with radical of codimension 1 is semisimple and 1-dimensional. On the other hand, there exist quasi-Hopf (in fact, Hopf) algebras, whose radical has codimension 2.…

We prove several results concerning quasi-bialgebra morphisms $\mathcal{D}^\omega(G)\to\mathcal{D}^\eta(H)$ of twisted group doubles. We take a particular focus on the isomorphisms which are simultaneously isomorphisms…

The article is devoted to the describtion of quasitriangular structures (universal R-matrices) on cocommutative Hopf algebras. It is known that such structures are concentrated on finite dimensional Hopf subalgebras. In particular,…

This paper defines a pairing of two finite Hopf C*-algebras $A$ and $B$, and investigates the interactions between them. If the pairing is non-degenerate, then the quantum double construction is given. This construction yields a new finite…

Family of doublings of Hopf algeras based on the product of algebra and its dual are constructed and studied. Special cases of these construction may be considered as natural quantum analogs of rings of differential operators on groups.…

Let $\mathsf{Rep}(H)$ be the category of finite-dimensional representations of a finite-dimensional Hopf algebra $H$. Andruskiewitsch and Mombelli proved in 2007 that each indecomposable exact $\mathsf{Rep}(H)$-module category has form…

In this paper we mainly construct bicrossproduct for finite-dimensional monoidal Hom-Hopf algebra $(H,\alpha)$, generalizing the Majid's bicrossproduct. Naturally the Hom-type bicrossproduct leads to Drinfel'd double $(H^{op}\bowtie…

We consider a class of quasi-Hopf algebras which we call \emph{generalized twisted quantum doubles}. They are abelian extensions $H = \mb{C}[\bar{G}] \bowtie \mb{C}[G]$ ($G$ is a finite group and $\bar{G}$ a homomorphic image), possibly…