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1.
Let A and B be multiplier Hopf algebras, and let R ∈ M(B ? A) be an anti-copairing multiplier, i.e, the inverse of R is a skew-copairing multiplier in the sense of Delvaux [5]. Then one can construct a twisted tensor coproduct multiplier Hopf algebra A ? R B. Using this, we establish the correspondence between the existence of quasitriangular structures in A ? R B and the existence of such structures in the factors A and B. We illustrate our theory with a profusion of examples which cannot be obtained by using classical Hopf algebras. Also, we study the class of minimal quasitriangular multiplier Hopf algebras and show that every minimal quasitriangular Hopf algebra is a quotient of a Drinfel’d double for some algebraic quantum group. 相似文献
2.
In this paper,we show that if H is a finite dimensional Hopf algebra then H is quasitri-angular if and only if H is coquasi-triangular. As a consequentility ,we obtain a generalized result of Sauchenburg. 相似文献
3.
准三角Hopf代数与双积 总被引:1,自引:0,他引:1
本文首先给出准三角Hopf代数与Yetter-Drinfeld模的关系,推广了Radford关于双积的构造,讨论二重Smash积与双积的关系. 相似文献
4.
Let p and q be odd prime numbers. It is shown that all quasitriangularHopf algebras of dimension pq over an algebraically closed fieldk of characteristic zero are semisimple and therefore isomorphicto a group algebra. 相似文献
5.
该文主要考虑了拟三角Hopf代数的某种Ore -扩张问题. 对拟三角Hopf代数的Ore -扩张何时保持相同的拟三角结构给出了充分必要条件. 最后作为应用, 文章讨论了Sweedler Hopf代数和Lusztig小量子群的Ore -扩张结构. 相似文献
6.
利用quiver方法确定了一个广义Taft代数具有拟三角Hopf结构当且仅当它是Sweedler 4维Hopf代数.用不同于文[15]的方法,对任意的正整数n,构造出一类拟三角Hopf代数H(n). 相似文献
7.
利用quiver方法确定了一个广义Taft代数具有拟三角Hopf结构当且仅当它是Sweedler 4维Hopf代数.用不同于文[15]的方法,对任意的正整数n,构造出一类拟三角Hopf代数H(n). 相似文献
8.
We compute the Drinfel’d double for the bicrossproduct multiplier Hopf algebra A = k[G] ⋊ K(H) associated with the factorization of an infinite group M into two subgroups G and H. We also show that there is a basis-preserving self-duality structure for the multiplier Hopf algebra A = k[G] ⋊ K(H) if there is a factor-reversing group isomorphism.
Presented by A. Verschoren. 相似文献
9.
L. Delvaux 《代数通讯》2013,41(1):346-360
In this article we lay the algebraic foundations to establish the existence of trace functions on infinite-dimensional (multiplier) Hopf algebras. We solve the problem within the framework of multiplier Hopf algebra with integrals. By applying this theory to group-cograded multiplier Hopf algebras, we prove the existence of group-traces on group-cograded multiplier Hopf algebras with possibly infinite-dimensional components. We generalize the results as obtained by Virelizier in the case of finite-type Hopf group-coalgebras. 相似文献
10.
Adriana Nenciu 《Algebras and Representation Theory》2004,7(2):159-172
We study the quasitriangular structures for a family of pointed Hopf algebras which is big enough to include Taft's Hopf algebras H
n
2, Radford's Hopf algebras H
N,n,q, and E(n). We give necessary and sufficient conditions for the Hopf algebras in our family to be quasitriangular. For the case when they are, we determine completely all the quasitriangular structures. Also, we determine the ribbon elements of the quasitriangular Hopf algebras and the quasi-ribbon elements of their Drinfel'd double. 相似文献
11.
The goal of this article is to generalize the theory of Hopf–Ore extensions on Hopf algebras to multiplier Hopf algebras. First the concept of a Hopf–Ore extension of a multiplier Hopf algebra is introduced. We give a necessary and sufficient condition for Ore extensions to become a multiplier Hopf algebra. Finally, *-structures are constructed on Hopf–Ore extensions, and certain isomorphisms between Hopf–Ore extensions are discussed. 相似文献
12.
本文引入两个概念,即,关于拟三角双代数的cylinder余代数和cylinder余积,并指出存在一个反余代数同构:(H,■)≌(H,■),其中(H,■)是cylinder余积,(H,■)是辫余积,对任意有限维Hopf代数H,我们证明Drinfel'd量子偶(D(H),■_(D(H)))是cylinder余积.设(H,H,R)是余配对Hopf代数,如果R∈Z(H■H),则通过两次扭曲,我们可以构造扭曲余代数(H~■)R~(-1),它的余乘法恰是cylinder余积.而且对任意的广义Long重模,通过cylinder扭曲,我们可以构造Yang-Baxter方程,四辫对和Long方程. 相似文献
13.
14.
《数学的实践与认识》2013,(16)
余积分是Hopf代数和乘子Hopf代数中的一类特殊元素,它的良好性质在研究Hopf代数的半单和余半单中有着很重要的作用.研究了乘子Hopf代数Ore扩张上的余积分,给出余积分的存在形式及其存在性. 相似文献
15.
Pairing and Quantum Double of Multiplier Hopf Algebras 总被引:2,自引:0,他引:2
We define and investigate pairings of multiplier Hopf (*-)algebras which are nonunital generalizations of Hopf algebras. Dual pairs of multiplier Hopf algebras arise naturally from any multiplier Hopf algebra A with integral and its dual Â. Pairings of multiplier Hopf algebras play a basic rôle, e.g., in the study of actions and coactions, and, in particular, in the relation between them. This aspect of the theory is treated elsewhere. In this paper we consider the quantum double construction out of a dual pair of multiplier Hopf algebras. We show that two dually paired regular multiplier Hopf (*-)algebras A and B yield a quantum double which is again a regular multiplier Hopf (*-)algebra. If A and B have integrals, then the quantum double also has an integral. If A and B are Hopf algebras, then the quantum double multiplier Hopf algebra is the usual quantum double. The quantum double construction for dually paired multiplier Hopf (*-)algebras yields new nontrivial examples of multiplier Hopf (*-)algebras. 相似文献
16.
Sonia Natale 《代数通讯》2013,41(12):4763-4775
We show that bicrossed product Hopf algebras arising from exact factorizations in almost simple finite groups, so in particular, in simple and symmetric groups, admit no quasitriangular structure. 相似文献
17.
In this paper, we introduce a generalized Hopf Galois theory for regular multiplier Hopf algebras with integrals, which might be viewed as a generalization of the Hopf Galois theory of finite-dimensional Hopf algebras. We introduce the notion of a coaction of a multiplier Hopf algebra on an algebra. We show that there is a duality for actions and coactions of multiplier Hopf algebras with integrals. In order to study the Galois (co)action of a multiplier Hopf algebra with an integral, we construct a Morita context connecting the smash product and the coinvariants. A Galois (co)action can be characterized by certain surjectivity of a canonical map in the Morita context. Finally, we apply the Morita theory to obtain the duality theorems for actions and coactions of a co-Frobenius Hopf algebra. 相似文献
18.
L. Delvaux 《Algebras and Representation Theory》2007,10(6):533-554
Let B be a regular multiplier Hopf algebra. Let A be an algebra with a non-degenerate multiplication such that A is a left B-module algebra and a left B-comodule algebra. By the use of the left action and the left coaction of B on A, we determine when a comultiplication on A makes A into a “B-admissible regular multiplier Hopf algebra.” If A is a B-admissible regular multiplier Hopf algebra, we prove that the smash product A # B is again a regular multiplier Hopf algebra. The comultiplication on A # B is a cotwisting (induced by the left coaction of B on A) of the given comultiplications on A and B. When we restrict to the framework of ordinary Hopf algebra theory, we recover Majid’s braided interpretation of Radford’s
biproduct.
Presented by K. Goodearl. 相似文献
19.
Let A be a regular multiplier Hopf algebra, and let Aut(A) denote the set of all isomorphisms α from A to itself that are algebra maps satisfying (Δ ○ α)(a) = (α ? α) ○ Δ(a) for all a ∈ A. Let G be a certain crossed product group Aut(A) × Aut(A). The main purpose of this article is to provide a class of new braided T-categories in the sense of Turaev [\citealp9]. For this, we introduce a class of new categories A 𝒴𝒟 A (α, β) of (α, β)-Yetter–Drinfel'd modules with α, β ∈Aut(A), and we show that the category ?𝒴𝒟(A) = { A 𝒴𝒟 A (α, β)}(α, β)∈G becomes a braided T-category over G, generalizing the main constructions by Panaite and Staic [6]. 相似文献
20.
We define the concept of “semiprime” for preradicals and for submodules, and we prove some properties that relate both of them. Related concepts are defined in article by Bican et al. [2] and by Van den Berg and Wisbauer [9]. For any ring, we compare the least semiprime preradical, the Jacobson radical and the join of all nilpotent preradicals, and we characterize V-rings in terms of these three preradicals. We study the least semiprime preradical above any preradical and we prove some of its properties. Using “Amitsur constructions” we define another related operators and prove some of their properties. 相似文献