Results 91 to 100 of about 12,045 (118)

Some ribbon elements for the quasi-Hopf algebra Dω(H)

, 2020
We construct an explicit isomorphism between the quasitriangular quasi-Hopf algebra Dω(H) defined in [D. Bulacu and F. Panaite, A generalization of the quasi-Hopf algebra Dω(G), Commun.
D. Bulacu, F. Panaite
semanticscholar   +1 more source

The quasitriangular structures for a class ofT-smash product Hopf algebras

Israel Journal of Mathematics, 2005
Let \(B\) and \(H\) be Hopf algebras, and \(T\colon H\otimes B\to B\otimes H\) a linear map. On \(B\otimes H\), we introduce a new multiplication \(m=(m_B\otimes m_H)\circ(B\otimes T\otimes H)\). We take the usual tensor coproduct comultiplication as comultiplication on \(B\otimes H\).
Zhengming Jiao
exaly   +3 more sources

Structure of quasitriangular quasi—hopf algebras

Functional Analysis and Its Applications, 1992
A quasi-Hopf algebra differs from a Hopf algebra in a weakened version of the coassociativity. (The definition of this ``weak coassociativity'' is motivated by conformal field theory). As well as the ``classical limit'' of a deformation Hopf algebra is a Lie bialgebra, the ``classical limit'' of a quasi-Hopf algebra over \(\mathbb{C}[[h]]\) which is a ...
openaire   +2 more sources

Non-simple quasitriangular Hopf algebras of dimension $$pq^2$$

manuscripta mathematica, 2022
All algebras considered in the review are assumed to be finite dimensional over an algebraically closed field \(\Bbbk\) of characteristic \(0\). For distinct odd primes \(p\), \(q\) such that \(p\equiv 1\bmod q\), a positive integer \(t\) such that \(t^q\equiv 1\bmod p\) and \(t\not\equiv 1\bmod p\), a primitive \(q\)th root \(\omega\) of unity in ...
Kun Zhou, Gongxiang Liu
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Quasitriangular weak multiplier Hopf algebras and quantum Yang–Baxter equations

Journal of Mathematics and Physics
In this paper we present a new approach to solutions to the quantum Yang–Baxter equation. We will introduce the notion of quasitriangular weak multiplier Hopf algebras unifying the known notions for quasitriangular weak Hopf algebras and quasitriangular ...
Ruolei Fu, Shuanhong Wang
semanticscholar   +1 more source

Quasitriangular Hopf Algebras of Dimension pq

Bulletin of the London Mathematical Society, 2002
Let p and q be odd prime numbers. It is shown that all quasitriangular Hopf algebras of dimension pq over an algebraically closed field k of characteristic zero are semisimple and therefore isomorphic to a group algebra.
openaire   +2 more sources

Maschke’s theorem for smash products of quasitriangular weak Hopf algebras

Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhai, Wen-juan, Zhang, Liang-yun
exaly   +3 more sources

Skew braces as remnants of co-quasitriangular Hopf algebras in SupLat

Journal of Algebra, 2021
Skew braces are sets with two compatible group structures and they have been introduced by \textit{L. Guarnieri} and \textit{L. Vendramin} [Math. Comput. 86, No. 307, 2519--2534 (2017; Zbl 1371.16037)] to study set-theoretical solutions of the Yang-Baxter equation.
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QUASITRIANGULAR STRUCTURES ON POINTED HOPF ALGEBRAS OF RANK ONE

JP Journal of Algebra, Number Theory and Applications, 2016
In the paper [J. Algebra 302, No. 1, 214--230 (2006; Zbl 1126.16028)], \textit{L. Krop} and \textit{D. E. Radford} gave the classification of finite dimensional pointed Hopf algebras of rank one over an algebraically closed field of characteristic zero in terms of certain \textit{group datum} \({\mathbf D} = (G, \chi, g, \mu)\), where \(G\) is a finite
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Quasitriangular Structures on Abelian Extensions of Z2 I

Algebra Colloquium
In this paper, we study quasitriangular structures on a class of semisimple Hopf algebras [Formula: see text] constructed through abelian extensions of [Formula: see text] by [Formula: see text] for an abelian group [Formula: see text].
Gongxiang Liu, K. Zhou
semanticscholar   +1 more source