Related papers: An approach to quasi-Hopf algebras via Frobenius c…
Drinfeld showed that any finite dimensional Hopf algebra \G extends to a quasitriangular Hopf algebra \D(\G), the quantum double of \G. Based on the construction of a so--called diagonal crossed product developed by the authors, we…
We construct the general supersymmetry algebra via the adjoint action on a semi-Hopf algebra which has a more general structure than a Hopf algebra. As a result we have an extended supersymmetry theory with quantum gauge group, i.e.,…
We study a natural construction of Hopf algebra quotients canonically associated to an R-matrix in a finite dimensional Hopf algebra. We apply this construction to show that a quasitriangular Hopf algebra whose dimension is odd and…
The problem of introducing a dependence of elements of quantum group on classical parameters is considered. It is suggested to interpret a homomorphism from the algebra of functions on quantum group to the algebra of sections of a sheaf of…
We study Frobenius eigenvalues of the compactly supported rigid cohomology of a variety defined over a finite field of $q$ elements via Dwork's method. A couple of arithmetic consequences will be drawn from this study. As the first…
In this work, the notion of a quantum inverse semigroup is introduced as a linearized generalization of inverse semigroups. Beyond the algebra of an inverse semigroup, which is the natural example of a quantum inverse semigroup, several…
We extend to the co-Frobenius case a result of Drinfeld and Radford related to the fourth power of the antipode of a finite dimensional (co)quasitriangular Hopf algebra.
We apply categorical machinery to the problem of defining anti-Yetter-Drinfeld modules for quasi-Hopf algebras. While a definition of Yetter-Drinfeld modules in this setting, extracted from their categorical interpretation as the center of…
A Lie version of Turaev's $\overline{G}$-Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a \textit{$\frak{g}$-quasi-Frobenius Lie algebra} for…
Rational Hopf algebras (certain quasitriangular weak quasi-Hopf $^*$-algebras) are expected to describe the quantum symmetry of rational field theories. In this paper methods are developped which allow for a classification of all rational…
The mod 2 Steenrod algebra $\mathcal{A}_2$ can be defined as the quotient of the mod 2 Leibniz--Hopf algebra $\mathcal{F}_2$ by the Adem relations. Dually, the mod 2 dual Steenrod algebra $\mathcal{A}_2^*$ can be thought of as a sub-Hopf…
We construct an example of a non-trivial homogeneous quasimorphism on the group of Hamiltonian diffeomorphisms of the two and four dimensional quadric hypersurfaces which is continuous with respect to both the $C^0$-metric and the Hofer…
We show that a large class of finite dimensional pointed Hopf algebras is quasi-isomorphic to their associated graded version coming from the coradical filtration, i.e. they are 2-cocycle deformations of the latter. This supports a slightly…
The Terwilliger algebras of association schemes over an arbitrary field $\mathbb{F}$ were called the Terwilliger $\mathbb{F}$-algebras of association schemes in [9]. In this paper, we study the Terwilliger $\mathbb{F}$-algebras of factorial…
A quasihomomorphism is a map that satisfies the homomorphism relation up to bounded error. Fujiwara and Kapovich proved a rigidity result for quasihomomorphisms taking values in discrete groups, showing that all quasihomomorphisms can be…
This is an introduction for algebraists to the theory of algebras and Hopf algebras in braided categories. Such objects generalise super-algebras and super-Hopf algebras, aswell as colour-Lie algebras. Basic facts about braided categories C…
We consider the universal solution of the Gervais-Neveu-Felder equation in the ${\cal U}_q(sl_2)$ case. We show that it has a quasi-Hopf algebra interpretation. We also recall its relation to quantum 3-j and 6-j symbols. Finally, we use…
We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We…
Any finite-dimensional Hopf algebra H is Frobenius and the stable category of H-modules is triangulated monoidal. To H-comodule algebras we assign triangulated module-categories over the stable category of H-modules. These module-categories…
We define total Frobenius-Schur indicator for each object in a spherical fusion category $C$ as a certain canonical sum of its higher indicators. The total indicators are invariants of spherical fusion categories. If $C$ is the…