弱量子代数wU_p(■)的弱Hopf代数结构

设G为有限维半单李代数,参数q不是单位根.定义了一个具有弱Hopf代数结构的弱量子代数wU_q(■),构造了它的类群元素集,并给出了两个不同参数的弱量子代数同构的条件.     

弱Hopf群T-余代数上的弱Doi-Hopf群模

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.     

广义弱群像代数

本文首先介绍了广义弱群像代数的概念, 并构造了一系列具体的例子, 通过例子可以看出有限群胚代数和群像代数都可以看作是广义弱群像代数; 接着本文证明了广义弱群像代数也可以看作是一类广义弱双Frobenius代数, 并探讨了广义弱双Frobenius代数成为有限群胚代数的条件; 最后本文给出了低维广义弱群像代数的具体结构.     

弱斜配对双代数和弱相关Long双代数

该文在弱双代数$H$上给出了扭曲积$(H^\sigma,\cdot_\sigma)$成为弱双代数的充分必要条件.设$[B, H, \tau]$是一个弱斜配对, 并且$\tau$可逆,则在某个条件下弱双交叉积$B\bowtie_\tau H$是一个弱双代数. 如果$(B,H, \sigma)$是弱相关Long双代数, 并且$\sigma$可逆,则弱双交叉积$B^{OP}\bowtie_\sigma H$可以被构造. 它的乘法是:$(x\otimes h)(y\otimes g)=\Sigma\sigma(y_1, h_1)y_2x\otimes h_2g\sigma^{-1}(y_3, h_3),$ 特别地, 如果$(B, H,\sigma)$是相关Long双代数, 则$(B^{OP \bowtie_\sigma H,\beta)$是Long双代数当且仅当对任意$b, d\in B^{OP}; g, \ell\in H$,$\Sigma\sigma^{-1}(b, g_2\ell)\sigma(d, g_1)=\Sigma\sigma^{-1}(b,\ell g_1)\sigma(d, g_2),$ 其中$B$为$H$的子Hopf代数,$\beta$定义为$\beta(b\bowtie_\sigma h\otimes c\bowtie_\sigma g)=\varepsilon_H(h)\varepsilon_{B^{OP}}(c)\sigma^{-1}(b, g).$ 对于Sweedler 4维Hopf代数$H$, 作者给出一个例子说明:此弱双交叉积$(B^{OP}\bowtie_\sigma H, \beta)$不仅是一个Long双代数,而且是一个非可换和非余可换的8维Hopf代数. 最后, 设$B,H$都是弱双代数, $\sigma: B\otimes H\rightarrow k$是一个线性映射, 作者给出了$(B,\sigma,\leftharpoonup, \Delta_B)$是弱相关右$(H, B)$ -重模代数的充分必要条件.     

弱H-模代数上的弱Galois扩张

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.     

弱模余代数的结构定理

设H为弱Hopf代数,C为弱右H-模余代数,令C=C/C·ker L.利用Smash余积来研究弱模余代数上的结构定理,并给出了C与C×H作为余代数同构的条件.     

弱Hopf群余代数Kegel定理

本文研究了余三角弱Hopfπ-余代数H的左弱π-H-余模代数.通过构造左弱π-H-余模代数的导出π-σ-李代数,得到了弱Hopf π-余代数Kegel定理,推广了文献[4]的结果.     

李超代数的弱C-理想及其相关性质

本文首先引入了李超代数的弱c-理想、弱c-单李超代数、弱c-理想可补的概念,然后研究了特征不为2,3的基域上李超代数与弱c-理想相关的一些结构性质,给出一个李超代数是弱c-单李超代数的充要条件,并利用Frattini理想,给出了李超代数的一个弱c-理想是其理想的充分条件,同时给出其商代数的子代数有子理想补的充要条件;最...     

弱Hopf代数作用与冲积

本文研究了弱Hopf代数上的冲积并讨论了它约性质．设H是弱Hopf代数,A是左H-摸代数．我们给出了冲积A#H是弱双代数的一个充分条件以及A#H是A可分扩张的一个判定条件．另外,利用积分理论研究了Hopf模代数的有限性条件．     

弱群余代数的交叉积

该文引入弱群交叉积的概念,并给出弱群交叉积代数和通常的张量积余代数构成弱半Hopf群余代数的充要条件,接着证明了弱群交叉积上的对偶定理,推广了沈和王~([7-8])的主要结果.     

Transmutation theory of a coquasitriangular weak Hopf algebra

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.     

The quantum double of a factorizable weak Hopf algebra

Let (H,R) be a finite dimensional quasitriangular weak Hopf algebra over a field k. We first construct a weak Hopf algebra [Δ(1)(H?H)Δ(1)]^R, which is based on the subalgebra of the tensor product algebra H?H. Next we verify that if H is factorizable, then the Drinfeld’s quantum double of H is isomorphic to [Δ(1)(H?H)Δ(1)]^R.     

Left-symmetric algebra structures on the twisted Heisenberg-Virasoro algebra

The compatible left-symmetric algebra structures on the twisted Heisenberg-Virasoro algebra with some natural grading conditions are completely determined. The results of the earlier work on left-symmetric algebra structures on the Virasoro algebra play an essential role in determining these compatible structures. As a corollary, any such left-symmetric algebra contains an infinite-dimensional nontrivial subalgebra that is also a submodule of the regular module.     

Extension of a quantized enveloping algebra by a Hopf algebra

Suppose that H is a Hopf algebra,and g is a generalized Kac-Moody algebra with Cartan matrix A =(aij)I×I,where I is an index set and is equal to either {1,2,...,n} or the natural number set N.Let f,g be two mappings from I to G(H),the set of group-like elements of H,such that the multiplication of elements in the set {f(i),g(i)|i ∈I} is commutative.Then we define a Hopf algebra Hgf Uq(g),where Uq(g) is the quantized enveloping algebra of g.     

The planar algebra associated to a Kac algebra

We obtain (two equivalent) presentations — in terms of generators and relations — of the planar algebra associated with the subfactor corresponding to (an outer action on a factor by) a finite-dimensional Kac algebra. One of the relations shows that the antipode of the Kac algebra agrees with the ‘rotation on 2-boxes’.     

Generalizing the notion of Koszul algebra

We introduce a generalization of the notion of a Koszul algebra, which includes graded algebras with relations in different degrees, and we establish some of the basic properties of these algebras. This class is closed under twists, twisted tensor products, regular central extensions and Ore extensions. We explore the monomial algebras in this class and we include some well-known examples of algebras that fall into this class.     

On Wiener type Banach algebra

A clarified study on the G-complete symmetry Banach algebra is given. A Wiener type Banach algebra as well as its stucture is introduced and studied. An application of this algebra is presented.     

On Fourier algebra homomorphisms

Let G be a locally compact group and let B(G) be the dual space of C∗(G), the group C∗ algebra of G. The Fourier algebra A(G) is the closed ideal of B(G) generated by elements with compact support. The Fourier algebras have a natural operator space structure as preduals of von Neumann algebras. Given a completely bounded algebra homomorphism we show that it can be described, in terms of a piecewise affine map with Y in the coset ring of H, as follows