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1.
在弱Hopf群余代数情形中,讨论了一簇从弱Doi-Hopf群模范畴到某个代数上的模范畴忘却函子的可分性,诱导出弱Doi-Hopf群模数据的正规化积分概念,证明了正规化积分存在性是忘却函子可分的判别准则.所得结果在弱量子Yetter-Drinfel'd群模范畴及弱相对Hopf群模范畴中有应用价值.  相似文献   

2.
该文首先引入了弱Hopf代数上的弱Alternative Doi-Hopf模,然后构造了从弱Alternative Doi-Hopf模范畴到模范畴(余模范畴)忘却函子的伴随函子.  相似文献   

3.
本文研究了Doi-Hopf模范畴中的sovereign结构,引入了sovereign Doi-Hopf数组和Doi-smash积的定义,证明了Doi-smash积的表示范畴与Doi-Hopf模范畴的等价性,并给出了Doi-Hopf模范畴做成sovereign范畴的充要条件.作为应用,研究了Yetter-Drinfeld模范畴中的sovereign结构.  相似文献   

4.
本文揭示了弱Doi-Hopf π-模范畴和弱Yetter-Drinfeld π-模范畴之间的密切联系,并证明了弱Yetter-Drinfeld π-模范畴同构于一个T-范畴的中心.  相似文献   

5.
贾玲  李方 《数学学报》2007,50(1):105-116
主要引入了弱entwined模上的弱度量,并用它来考虑两个弱entwined模范畴之间约函子关系.同时还给出了弱entwined模的Frobenius性质和Maschke型定理.  相似文献   

6.
弱Hopf群T-余代数上的弱Doi-Hopf群模   总被引:2,自引:1,他引:1  
在弱Hopf群T-余代数情形下,弱量子Yetter-Drinfeld群模的概念被引入,并证明了弱量子Yetter-Drinfeld群模是特殊的弱Doi-Hopf群模.接着建立了弱量子Yetter Drinfeld群模范畴与弱Hopf群双余模代数的余不动点子代数B上模范畴之间的伴随对.最后考虑了弱量子Yetter-Drinfeld群模的积分.  相似文献   

7.
张良云  祝家贵  佟文廷 《数学学报》2003,46(6):1143-115
本文引入了扭曲余模概念,给出了由扭曲余模构造的扭曲Hopf模的判别条件及其基本结构定理,引入了相关Yetter-Drinfel’d模概念(它是Yetter-Drinfel’d模概念的自然推广),证明了相关Yetter-Drinfel’d模范畴是预辫monoidal范畴,指出了由Yetter-Drinfel’d模通过扭曲余模构作的模恰是相关Yetter-Drinfel’d模.  相似文献   

8.
该文研究了群缠绕模范畴怎样构造成张量范畴,给出的充分条件是要求群缠绕模中的代数和群余代数分别是双代数和半-Hopf群余代数,并满足一些相容条件.作者在张量群缠绕模范畴上构造了辫子.该文结果包括了拟三角和余拟三角Hopf代数(Hopf群余代数),Doi-Hopf群模等情况.  相似文献   

9.
设u~(≥0)表示一个固定单李代数的半量子群,给出了u~(≥0)的性质和表示.证明了Hopf代数u~(≥0)不是拟余交换的,因此左u~(≥0)-模范畴不是辫子monoidal范畴.在权模范畴W中,给出了所有单对象和投射对象.最后描述了所有单的Yetter-Drinfel'd u~(≥0)-权模.  相似文献   

10.
主要讨论扭曲Smash余积余模范畴c×Hll,得到c×Hll是辫monoidal范畴的一个充要条件.  相似文献   

11.
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   

12.
We discuss properties of Yetter-Drinfeld modules over weak bialgebras over commutative rings. The categories of left-left, left-right, right-left and right-right Yetter-Drinfeld modules over a weak Hopf algebra are isomorphic as braided monoidal categories. Yetter-Drinfeld modules can be viewed as weak Doi-Hopf modules, and, a fortiori, as weak entwined modules. IfH is finitely generated and projective, then we introduce the Drinfeld double using duality results between entwining structures and smash product structures, and show that the category of Yetter-Drinfeld modules is isomorphic to the category of modules over the Drinfeld double. The category of finitely generated projective Yetter-Drinfeld modules over a weak Hopf algebra has duality.  相似文献   

13.
In this paper,we introduce several centralizer constructions in a monoidal context and establish a monoidal equivalence with the category of Yetter–Drinfeld modules over a weak braided Hopf monoid.We apply the general result to the calculus of the center in module categories.  相似文献   

14.
It is a key property of bialgebras that their modules have a natural tensor product. More precisely, a bialgebra over k can be characterized as an algebra H whose category of modules is a monoidal category in such a way that the underlying functor to the category of k-vector spaces is monoidal (i.e. preserves tensor products in a coherent way). In the present paper we study a class of algebras whose module categories are also monoidal categories; however, the underlying functor to the category of k-vector spaces fails to be monoidal. Instead, there is a suitable underlying functor to the category of B-bimodules over a k-algebra B which is monoidal with respect to the tensor product over B. In other words, we study algebras L such that for two L-modules V and W there is a natural tensor product, which is the tensor product VBW over another k-algebra B, equipped with an L-module structure defined via some kind of comultiplication of L. We show that this property is characteristic for ×B-bialgebras as studied by Sweedler (for commutative B) and Takeuchi. Our motivating example arises when H is a Hopf algebra and A an H-Galois extension of B. In this situation, one can construct an algebra L:=L(A,H), which was previously shown to be a Hopf algebra if B=k. We show that there is a structure theorem for relative Hopf bimodules in the form of a category equivalence . The category on the left hand side has a natural structure of monoidal category (with the tensor product over A) which induces the structure of a monoidal category on the right hand side. The ×B-bialgebra structure of L that corresponds to this monoidal structure generalizes the Hopf algebra structure on L(A,H) known for B=k. We prove several other structure theorems involving L=L(A,H) in the form of category equivalences .  相似文献   

15.
Entwined modules arose from the coalgebra-Galois theory. They are a generalisation of unified Doi-Hopf modules. In this paper, Frobenius properties and Maschke-type theorems known for Doi-Hopf modules are extended to the case of entwined modules.

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16.
Module categories,weak Hopf algebras and modular invariants   总被引:6,自引:0,他引:6  
We develop a theory of module categories over monoidal categories (this is a straightforward categorization of modules over rings). As applications we show that any semisimple monoidal category with finitely many simple objects is equivalent to the category of representations of a weak Hopf algebra (theorem of T. Hayashi) and we classify module categories over the fusion category of sl(2) at a positive integer level where we meet once again the ADE classification pattern.  相似文献   

17.
缠绕模的辫子范畴   总被引:1,自引:0,他引:1       下载免费PDF全文
该文给出了缠绕模范畴成为辫子范畴的充分必要条件.  相似文献   

18.
本文研究了弱Hopf代数的扭曲理论的对偶问题.利用了弱Hopf代数上的弱Hopf双模的(辫子)张量范畴与扭曲弱Hopf代数上的弱Hopf双模的(辫子)张量范畴等价方法,得到Long模范畴是Yetter-Drinfel'd模范畴的辫子张量子范畴.推广了Oeckl(2000)的结果.  相似文献   

19.

We exhibit the cartesian differential categories of Blute, Cockett and Seely as a particular kind of enriched category. The base for the enrichment is the category of commutative monoids—or in a straightforward generalisation, the category of modules over a commutative rig k. However, the tensor product on this category is not the usual one, but rather a warping of it by a certain monoidal comonad Q. Thus the enrichment base is not a monoidal category in the usual sense, but rather a skew monoidal category in the sense of Szlachányi. Our first main result is that cartesian differential categories are the same as categories with finite products enriched over this skew monoidal base. The comonad Q involved is, in fact, an example of a differential modality. Differential modalities are a kind of comonad on a symmetric monoidal k-linear category with the characteristic feature that their co-Kleisli categories are cartesian differential categories. Using our first main result, we are able to prove our second one: that every small cartesian differential category admits a full, structure-preserving embedding into the cartesian differential category induced by a differential modality (in fact, a monoidal differential modality on a monoidal closed category—thus, a model of intuitionistic differential linear logic). This resolves an important open question in this area.

  相似文献   

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