共查询到20条相似文献,搜索用时 46 毫秒
1.
Q.-G. Chen 《代数通讯》2013,41(1):310-335
This article is devoted to constructing a class of coquasitriangular Hopf group algebras. First, we introduce the notion of group unified product. Then we prove the classification theorem for group unified products and discuss the sufficient and necessary conditions to make the group unified product to be a coquasitriangular Hopf group-algebra. Finally, some applications of the main results are considered. 相似文献
2.
In this paper, we define the notion of self-dual graded weak Hopf algebra and self-dual semilattice graded weak Hopf algebra. We give characterization of finite-dimensional such algebras when they are in structually simple forms in the sense of E. L. Green and E. N. Morcos. We also give the definition of self-dual weak Hopf quiver and apply these types of quivers to classify the finite- dimensional self-dual semilattice graded weak Hopf algebras. Finally, we prove partially the conjecture given by N. Andruskiewitsch and H.-J. Schneider in the case of finite-dimensional pointed semilattice graded weak Hopf algebra H when grH is self-dual. 相似文献
3.
We give the necessary and sufficient conditions for a family of Brzezínski crossed product algebras with suitable comultiplication and counit to be a Hopf π-coalgebra. On the other hand, necessary and sufficient conditions for the Brzeziński π-crossed product A?H to be a coquasitriangular Hopf π-coalgebra are derived, then the category A?H ? of the left π-comodules over A?H is braided. 相似文献
4.
We investigate how the category of Doi-Hopf modules can be made into a monoidal category. It suffices that the algebra and coalgebra in question are both bialgebras with some extra compatibility relation. We study tensor identies for monoidal categories of Doi-Hopf modules. Finally, we construct braidings on a monoidal category of Doi-Hopf modules. Our construction unifies quasitriangular and coquasitriangular Hopf algebras, and Yetter-Drinfel'd modules. 相似文献
5.
Phng H
Hi 《Journal of Pure and Applied Algebra》1999,140(3):3199
Central bialgebras in a braided category
are algebras in the center of the category of coalgebras in
. On these bialgebras another product can be defined, which plays the role of the opposite product. Hence, coquasitriangular structures on central bialgebras can be defined. We prove some properties of the antipode on coquasitriangular central Hopf algebras and give a characterization of central bialgebras. 相似文献
6.
Quiver Hopf algebras 总被引:1,自引:0,他引:1
In this paper we study subHopfalgebras of graded Hopf algebra structures on a path coalgebra kQc. We prove that a Hopf structure on some subHopfquivers can be lifted to a Hopf structure on the whole Hopf quiver. If Q is a Schurian Hopf quiver, then we classified all simple-pointed subHopfalgebras of a graded Hopf structure on kQc. We also prove a dual Gabriel theorem for pointed Hopf algebras. 相似文献
7.
Let H be a Hopf algebra with a finite-dimensional, nontrivial space of skew primitive elements, over an algebraically closed field of characteristic zero. We prove that H contains either the polynomial algebra as a Hopf subalgebra, or a certain Schurian simple-pointed Hopf subalgebra. As a consequence, a complete list of the locally finite, simple-pointed Hopf algebras is obtained. Also, the graded automorphism group of a Hopf algebra on a Schurian Hopf quiver is determined, and the relation between this group and the automorphism groups of the corresponding Hopf quiver, is clarified. 相似文献
8.
9.
Basic Hopf algebras and quantum groups 总被引:10,自引:0,他引:10
This paper investigates the structure of basic finite dimensional Hopf algebras H over an algebraically closed field k. The algebra H is basic provided H modulo its Jacobson radical is a product of the field k. In this case H is isomorphic to a path algebra given by a finite quiver with relations. Necessary conditions on the quiver and on the coalgebra
structure are found. In particular, it is shown that only the quivers given in terms of a finite group G and sequence of elements of G in the following way can occur. The quiver has vertices and arrows , where the set is closed under conjugation with elements in G and for each g in G, the sequences W and are the same up to a permutation. We show how is a kG-bimodule and study properties of the left and right actions of G on the path algebra. Furthermore, it is shown that the conditions we find can be used to give the path algebras themselves a Hopf algebra structure (for an arbitrary field k). The results are also translated into the language of coverings. Finally, a new class of finite dimensional basic Hopf algebras
are constructed over a not necessarily algebraically closed field, most of which are quantum groups. The construction is not
characteristic free. All the quivers , where the elements of W generates an abelian subgroup of G, are shown to occur for finite dimensional Hopf algebras. The existence of such algebras is shown by explicit construction.
For closely related results of Cibils and Rosso see [Ci-R].
Received August 15, 1994; in final form May 16, 1997 相似文献
10.
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
11.
Let H be a coquasitriangular quantum groupoid. In this paper, using a suitable idempotent element e in H, we prove that eH is a braided group (or a braided Hopf algebra in the category of right H-comodules), which generalizes Majid’s transmutation theory from a coquasitriangular Hopf algebra to a coquasitriangular weak
Hopf algebra. 相似文献
12.
13.
Rachel Taillefer 《K-Theory》2001,24(1):69-85
A cyclic cohomology theory adapted to Hopf algebras has been introduced recently by Connes and Moscovici. In this paper, we consider this object in the homological framework, in the spirit of Loday and Quillen and Karoubi's work on the cyclic homology of associative algebras. In the case of group algebras, we interpret the decomposition of the classical cyclic homology of a group algebra in terms of this homology. We also compute both cyclic homologies for truncated quiver algebras. 相似文献
14.
The motivation of this paper is to study the natural quiver of an artinian algebra, a new kind of quivers, as a tool independing
upon the associated basic algebra. In Li (J Aust Math Soc 83:385–416, 2007), the notion of the natural quiver of an artinian algebra was introduced and then was used to generalize the Gabriel theorem
for non-basic artinian algebras splitting over radicals and non-basic finite dimensional algebras with 2-nilpotent radicals
via pseudo path algebras and generalized path algebras respectively. In this paper, firstly we consider the relationship between
the natural quiver and the ordinary quiver of a finite dimensional algebra. Secondly, the generalized Gabriel theorem is obtained
for radical-graded artinian algebras. Moreover, Gabriel-type algebras are introduced to outline those artinian algebras satisfying
the generalized Gabriel theorem here and in Li (J Aust Math Soc 83:385–416, 2007). For such algebras, the uniqueness of the related generalized path algebra and quiver holds up to isomorphism in the case
when the ideal is admissible. For an artinian algebra, there are two basic algebras, the first is that associated to the algebra
itself; the second is that associated to the correspondent generalized path algebra. In the final part, it is shown that for
a Gabriel-type artinian algebra, the first basic algebra is a quotient of the second basic algebra. In the end, we give an
example of a skew group algebra in which the relation between the natural quiver and the ordinary quiver is discussed. 相似文献
15.
16.
Kenichi Shimizu 《Algebras and Representation Theory》2012,15(2):325-357
We study Frobenius–Schur indicators of the regular representations of finite-dimensional semisimple Hopf algebras, especially
group-theoretical ones. Those of various Hopf algebras are computed explicitly. In view of our computational results, we formulate
the theorem of Frobenius for semisimple Hopf algebras and give some partial results on this problem. 相似文献
17.
LIU Gongxiang & YE Yu Institute of Mathematics Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China Department of Mathematics University of Science Technology of China Hefei China 《中国科学A辑(英文版)》2006,49(3):320-329
In this paper, we study the structures of monomial Hopf algebras over a field of positive characteristic. A necessary and sufficient condition for the monomial coalgebra Cd(n) to admit Hopf structures is given here, and if it is the case, all graded Hopf structures on Cd(n) are completely classified. Moreover, we construct a Hopf algebras filtration on Cd(n) which will help us to discuss a conjecture posed by Andruskiewitsch and Schneider. Finally combined with a theorem by Montgomery, we give the structure theorem for all monomial Hopf algebras. 相似文献
18.
本文研究并刻画了弱Hopf代数的余枢纽元,给出了其余表示伴有枢纽结构的等价条件,并刻画了余枢纽元和余带状元之间的关系,给出了相对应的Deligne型定理. 相似文献
19.
20.
A New Cyclic Module for Hopf Algebras 总被引:2,自引:0,他引:2
We define a new cyclic module, dual to the Connes–Moscovici cocyclic module, for Hopf algebras, and give a characteristic map for coactions of Hopf algebras. We also compute the resulting cyclic homology for cocommutative Hopf algebras, and some quantum groups. 相似文献