Related papers: Pentagon equation and matrix bialgebras
We study the pointed or copointed liftings of Nichols algebras associated to affine racks and constant cocycles for any finite group admitting a principal YD-realization of these racks. In the copointed case we complete the classification…
This article introduces a method, which starting from simple and quite general mathematical data, allows to construct linear algebras of operators which are, each of them, endowed with a bialgebra structure (coproduct and counity). Moreover…
Coactions of Hopf C*-bimodules simultaneously generalize coactions of Hopf C*-algebras and actions of groupoids. Following an approach of Baaj and Skandalis, we construct reduced crossed products and establish a duality for fine coactions.…
A general theory of matrix-spherical functions for dual Hopf algebras and right coideal subalgebras is developed. We establish their existence and define their orthogonality relations. When specialized to Kolb and Letzter's quantum…
We prove a general result on presentations of finitely-generated algebras and apply it to obtain nice presentations for some noncommutative algebras arising in the matrix bispectral problem. By "nice presentation" we mean a presentation…
We revisit a class of examples described in the original paper on biproducts, expand the class, and provide a detailed analysis of the coalgebra and algebra structures of many of these examples. Connections with the semisimple Hopf algebras…
We analyze the effect of pivotal structures (on a 2-category) on the planar algebra associated to a 1-cell as in \cite{Gho08} and come up with the notion of {\em perturbations of planar algebras by weights} (a concept that appeared earlier…
In this review article the construction of first order coordinate differential calculi on finitely generated and finitely related associative algebras are considered and explicit construction of the bimodule of one form over such algebras…
We construct algebraic cycles in Bloch's cubical cycle group which correspond to multiple polylogarithms with generic arguments. Moreover, we construct out of them a Hopf subalgebra in the Bloch-Kriz cycle Hopf algebra. In the process, we…
We introduce the bicategory of bialgebras with coverings (which can be thought of as coalgebra-indexed families of morphisms), and provide a motivating application to the transfer of formulas for primitives and antipode. Additionally, we…
This is a report on the present state of the problem of determining the dimension of the Nichols algebra associated to a rack and a cocycle. This is relevant for the classification of finite-dimensional complex pointed Hopf algebras whose…
We describe in which ways the Radford biproducts of certain eight-dimensional Yetter-Drinfel'd Hopf algebras over the elementary abelian group of order 4 can be written as extensions of Hopf algebras.
We provide isomorphism results for Hopf algebras that are obtained as graded twistings of function algebras on finite groups by cocentral actions of cyclic groups. More generally , we also consider the isomorphism problem for…
Faithful representations of regular $\ast$-rings and modular complemented lattices with involution within orthosymmetric sesquilinear spaces are studied within the framework of Universal Algebra. In particular, the correspondence between…
The paper develops the method for construction of the families of particular solutions to the nonlinear Partial Differential Equations (PDE) without relation to the complete integrability. Method is based on the specific link between…
We show that solutions of Pentagon equations lead to solutions of the Tetrahedron equation. The result is obtained in the spectral parameter dependent case.
We establish some new theorems on pentagon and pentagram.
The possibility of extending operations of topological and semitopological algebras to their Stone-\v{C}ech compactification and factorization of continuous functions through homomorphisms to metrizable algebras are investigated. Most…
New types of bialgebras arising from the Hopf equation (pentagonal equation) are introduced and studied. They will play from the Hopf equation the same role as the co-quasitriangular do from the quantum Yang Baxter equation.
Bialgebroids, separable bialgebroids, and weak Hopf algebras are compared from a categorical point of view. Then properties of weak Hopf algebras and their applications to finite index and finite depth inclusions of von Neumann algebras are…