共查询到18条相似文献,搜索用时 78 毫秒
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.
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
3.
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
4.
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
5.
《数学物理学报(A辑)》2010,(6)
该文给出了弱相关Hopf模范畴和余不变子模范畴之间的关系,以及余不变函子(·)~(coH)有和诱导Ind=·_B A的一些应用,并且证明了弱相关Hopf模范畴_AM~(H*)同构于弱smash积模范畴_(A#H)M. 相似文献
6.
本文研究了monoidal entwined模范畴上的张量积恒等式.利用了monoidal entwined模范畴的性质及Doi-Hopf模范畴上的张量积恒等式的研究方法,获得了monoidal entwined模范畴上的一些张量积恒等式,并证明了entwined模范畴有足够的内射对象,结果推广了Doi-Hopf模范畴的结论. 相似文献
7.
本文研究了弱模代数上的弱Galois扩张问题,利用不变子函子与积分方法,获得了弱Galois扩张的一个充分必要条件,推广了Cohen,Fishman和Montgomery的对应结果. 相似文献
8.
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
9.
10.
本文介绍了弱T-代数的概念并讨论了它的一些性质,同时给出了弱Yetter-Drinfeld群模的一个充分必要条件,并且证明了弱Yetter-Drinfeld群模事实上是一种弱Doi-Hopf群模.这些结果推广了由Caenepeel-Militaru-Zhu(1997)给出的定理. 相似文献
11.
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
12.
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
13.
The paper is concerned with endomorphism algebras for weak Doi-Hopf modules. Under the condition “weak Hopf-Galois extensions”,
we present the structure theorem of endomorphism algebras for weak Doi-Hopf modules, which extends Theorem 3.2 given by Schneider
in [1]. As applications of the structure theorem, we obtain the Kreimer-Takeuchi theorem (see Theorem 1.7 in [2]) and the
Nikshych duality theorem (see Theorem 3.3 in [3]) in the case of weak Hopf algebras, respectively. 相似文献
14.
Edgar E. Enochs Juan Martí nez Herná ndez Alberto del Valle 《Proceedings of the American Mathematical Society》1998,126(6):1611-1620
The category of left modules over right coherent rings of finite weak global dimension has several nice features. For example, every left module over such a ring has a flat cover (Belshoff, Enochs, Xu) and, if the weak global dimension is at most two, every left module has a flat envelope (Asensio, Martínez). We will exploit these features of this category to study its objects. In particular, we will consider orthogonal complements (relative to the extension functor) of several classes of modules in this category. In the case of a commutative ring we describe an idempotent radical on its category of modules which, when the weak global dimension does not exceed 2, can be used to analyze the structure of the flat envelopes and of the ring itself.
15.
Quan-guo Chen Shuan-hong Wang 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2011,81(2):261-272
Let π be a discrete group. Given a Doi-Hopf π-datum (H,A,C) and α∈π, we give necessary and sufficient conditions for the functor F
(α) from the category of Doi-Hopf π-modules to the category of right A
α
-modules to be separable. This leads to a generalized notion of integrals. As an application, we prove a Maschke type theorem
for Doi-Hopf π-modules and relative Hopf π-modules. 相似文献
16.
Lixin Mao 《Mediterranean Journal of Mathematics》2013,10(2):655-676
A functor of the functor category ((R-mod)op, Ab) is said to be strongly flat (resp. Ω-Mittag-Leffler) if any morphism from any finitely generated functor to it factors through a representable (resp. finitely presented) functor. We investigate the properties of strongly flat and Ω-Mittag-Leffler functors, which are generalizations of analogous classical module-theoretic properties. 相似文献
17.
Let π be a discrete group. Given a weak π-entwining structure \({(A,C)_{\pi - \psi }}\) and α ∈ π, we give the necessary and sufficient conditions for the forgetful functor \({F^{(\alpha )}}\) from the category \(U_A^{\pi - C}(\psi )\) of right \({(A,C)_{\pi - \psi }}\) -modules to the category \({M_{{A_\alpha }}}\) of right \({A_\alpha }\) -modules to be separable. This leads to a generalized notion of integrals. The results are applied to weak Doi-Hopf π-modules and to weak entwining modules. 相似文献
18.
We study monoidal structures on the category of (co)modules over a weak bialgebra. Results due to Nill and Szlachányi are unified and extended to infinite algebras. We discuss the coalgebra structure on the source and target space of a weak bialgebra. 相似文献