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51.
52.
For k a commutative ring, H a k‐bialgebra and A a right H‐comodule k‐algebra, we define a new multiplication on the H‐comodule A to obtain a twisted algebra” AT, T sumHom(H,End (A)). If T is convolution invertible, the categories of relative right Hopf modules over A and ATare isomorphic. Similarly a convolution invertible left twisting gives an isomorphism of the categories of relative left Hopf modules. We show that crossed products are invertible twistings of the tensor product, and obtain, as a corollary, a duality theorem for crossed products 相似文献
53.
Let H be a finite-dimensional Hopf algebra and A a finite-dimensional H-simple left H-module algebra. We show that the smash product A#H is isomorphic to End A′(V ? H*), where V ≠ 0 is a finite-dimensional left A-module and (A′, V′) the stabilizer of (A, V). As an application it is proved that A#H is isomorphic to a full matrix algebra over A′ when H is semisimple and dim V|dim A. 相似文献
54.
We introduce the concept of an object with the (finite) exchange property in an arbitrary Grothendieck category, and we present the basic properties of such an object. Applications are given for categories of graded modules and for categories of comodules over a coalgebra. Among other results, it is proved that an arbitrary coalgebra 𝒞 over a field has the finite exchange property. 相似文献
55.
ALONSO LVAREZ Jos Nicanor FERNNDEZ VILABOA Jos Manuel GONZLEZ RODRíIGUEZ Ramón SONEIRA CALVO Carlos 《中国科学 数学(英文版)》2011,(5)
In this paper we study the projections of weak braided Hopf algebras using the notion of Yetter-Drinfeld module associated with a weak braided Hopf algebra. As a consequence, we complete the study ofthe structure of weak Hopf algebras with a projection in a braiding setting obtaining a categorical equivalencebetween the category of weak Hopf algebra projections associated with a weak Hopf algebra H living in abraided monoidal category and the category of Hopf algebras in the non-strict braided monoidal cate... 相似文献
56.
Let k be an algebraically closed field of characteristic zero, and D
n
be the dihedral group of order 2n, where n is a positive even integer. In this paper, we investigate Yetter-Drinfeld modules over the Hopf-Ore extension A(n, 0) of kD
n
. We describe the structures and properties of simple Yetter-Drinfeld modules over A(n, 0), and classify all simple Yetter-Drinfeld modules over A(n, 0). 相似文献
57.
Serhii V. Gryshchuk Sergiy A. Plaksa 《Mathematical Methods in the Applied Sciences》2016,39(11):2939-2952
We consider a commutative algebra over the field of complex numbers with a basis {e1,e2} satisfying the conditions , . Let D be a bounded domain in the Cartesian plane xOy and Dζ={xe1+ye2:(x,y)∈D}. Components of every monogenic function Φ(xe1+ye2) = U1(x,y)e1+U2(x,y)ie1+U3(x,y)e2+U4(x,y)ie2 having the classic derivative in Dζ are biharmonic functions in D, that is, Δ2Uj(x,y) = 0 for j = 1,2,3,4. We consider a Schwarz‐type boundary value problem for monogenic functions in a simply connected domain Dζ. This problem is associated with the following biharmonic problem: to find a biharmonic function V(x,y) in the domain D when boundary values of its partial derivatives ?V/?x, ?V/?y are given on the boundary ?D. Using a hypercomplex analog of the Cauchy‐type integral, we reduce the mentioned Schwarz‐type boundary value problem to a system of integral equations on the real axes and establish sufficient conditions under which this system has the Fredholm property. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
58.
Application of homotopy analysis method for solving a class of nonlinear Volterra-Fredholm integro-differential equations 下载免费PDF全文
Sh. Sadigh Behzadi S. Abbasbandy A. Yildirim 《Journal of Applied Analysis & Computation》2012,2(2):127-136
In this paper, the nonlinear Volterra-Fredholm integro-differential equations are solved by using the homotopy analysis method (HAM). The approximation solution of this equation is calculated in the form of a series which its components are computed easily . The existence and uniqueness of the solution and the convergence of the proposed method are proved. A numerical example is studied to demonstrate the accuracy of the presented method. 相似文献
59.
本文讨论了将分式环S-1R上的模归约到R上的模时包(hull)、类(class)、界(bound)、秩(rank)的保持性,证明了:1)NR是A在MR中的包当且仅当NS-1R是A在MS-1R中的包;2)还讨论了分式模(S-1M)S-1R与MR之间上述性质存在单向或双向保持性的条件. 相似文献
60.
We classify the compatible left‐symmetric algebraic structures on the Witt algebra satisfying certain non‐graded conditions. It is unexpected that they are Novikov algebras. Furthermore, as applications, we study the induced non‐graded modules of the Witt algebra and the induced Lie algebras by Novikov‐Poisson algebras’ approach and Balinskii‐Novikov's construction. 相似文献