代数三角混合拉格朗日插值法

本文讨论代数多项式与三角多项式混合Ｌａｇｒａｎｇｅ插值问题，证明了这种插值问题的唯一可解性，给出了余项估计．数值算例表明这种插值方法的有效性．

AF vN代数中三角子代数的Lie理想

描述了AF von Neumann代数B中对角为Cartan子代数D的σ-弱闭三角子代数A的σ-弱闭Lie理想。证明了A中的σ-弱闭空间L是A的Lie理想当且仅当存在A的σ弱闭结合理想K和D的子空间Z使得K L K+Z。

π-quasitriangular group-cograded multiplier Hopf algebras

Let G be a group and （A, B） be a pair of multiplier Hopf algebras, where B is regular G-cograded. Let π be a crossing action of G on B, D^π=A^cop∝B=＋p∈GDπ^p with Dπ^p=A^cop∝Bp, is the Drinfeld double of the pair （A, B）, and then the deformation D^π becomes a multiplier Hopf algebra. B×A can be considered as a subalgebra of M（D^π×D^π）, the image of element b×a in B×A is （1∝b）×（a∝1） in M（D^π×D^π）. Let W =∑αWα∈ M（B×A） be a π-canonical multiplier for the pair （A, B） with Wα∈M（Bα×A） for all α∈G. The image of W in M（D^π×D^π）is a π-quasitriangular structure over D^π.

A note on ribbon elements of Hopf group-coalgebras

Let G be a discrete group with a neutral element and H be a quasitriangular Hopf G-coalgebra over a field k. Then the relationship between G-grouplike elements and ribbon elements of H is considered. First, a list of useful properties of a quasitriangular Hopf G-coalgebra and its Drinfeld elements are proved. Secondly, motivated by the relationship between the grouplike and ribbon elements of a quasitriangular Hopf algebra, a special kind of G-grouplike elements of H is defined. Finally, using the Drinfeld elements, a one-to-one correspondence between the special G-grouplike elements defined above and ribbon elements is obtained.

Decomposition of Jordan automorphism of two-order upper triangular matrix algebra over certain semilocal rings

Let T(R) be a two-order upper matrix algebra over the semilocal ring R which is determined by R=F×F where F is a field such that CharF=0. In this paper, we prove that any Jordan automorphism of T(R) can be decomposed into a product of involutive, inner and diagonal automorphisms.

Constructing generalized Drinfel'd quantum double

Let H be a Hopf algebra and B an algebra with two linear maps δ, τ： H H→B. The necessary and sufficient conditions for the twisted crossed product B#^τδH equipped with the tensor product coalgebra structure to be a bialgebra are proved. Then, B#^τδH is a coquasitriangular Hopf algebra under certain conditions. This coquasitriangular Hopf algerbra generalizes some known cross products. Finally, as an application, an explicit example is given.

The quasitriangular structures of biproduct Hopf algebras

The construction of the biproduct of Hopf algebras, which consists of smash product and the dual notion of smash coproduct, was first formulated by Radford. In this paper we study the quasitriangular structures over biproduct Hopf algebras B*H. We show the necessary and sufficient conditions for biproduct Hopf algebras to be quasitriangular. For the case when they are, we determine completely the unique formula of the quasitriangular structures. And so we find a way to construct solutions of the Yang-Baxter equation over biproduct Hopf algebras in the sense of (Majid, 1990).

Upper Triangular Matrix of Lie Algebra and a New Discrete Integrable Coupling System

The upper triangular matrix of Lie algebra is used to construct integrable couplings of discrete solition equations. Correspondingly, a feasible way to construct integrable couplings is presented. A nonlinear lattice soliton equation spectral problem is obtained and leads to a novel hierarchy of the nonlinear lattice equation hierarchy. It indicates that the study of integrable couplings using upper triangular matrix of Lie algebra is an important step towards constructing integrable systems.

A Characterization of Quasitriangular Hopf Algebras

In this paper,we show that if H is a finite dimensional Hopf algebra then H is quasitri-angular if and only if H is coquasi-triangular. As a consequentility ,we obtain a generalized result of Sauchenburg.

Constructions with Numbers

Pascal Triangle is more of a number construction （body） then an array of the binomial coefficients. It is a mathematical body, like the digital code feeds for computer but with 2 dimensions. And there should be bodies with x-dimensions and even abnormal or irregular appearances.

A note on the equivalence of m-periodic derived categories

Let A and B be finite-dimensional algebras over a field k of finite global dimension. Using some results of Gorsky in "Semi-derived Hall algebras and tilting invariance of Bridgeland-Hall algebras",we prove that if A and B are derived equivalent,then the corresponding m-periodic derived categories are triangulated equivalent.

Cohen-Fischman-Westreich's Double Centralizer Theorem for Almost-Triangular Hopf Algebras

In this paper, the authors study the Cohen-Fischman-Westreich's double centralizer theorem for triangular Hopf algebras in the setting of almost-triangular Hopf algebras.

On maximal non-selfadjoint reflexive algebras associated with a double triangle lattice

We show that the reflexive algebra Alg(L) given by a double triangle lattice L in a finite factor M(with L" = M) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diagonal subalgebra Alg(L) ∩ Alg(L)^+.Our method can be used to prove similar results in finite-dimensional matrix algebras.As a consequence,we give a new proof to the main theorem by Hou and Zhang(2012).

Quasi-triangular Hopf algebras and invariant Jacobians

We show that two module homomorphisms for groups and Lie algebras established by Xi(2012)can be generalized to the setting of quasi-triangular Hopf algebras.These module homomorphisms played a key role in his proof of a conjecture of Yau(1998).They will also be useful in the problem of decomposition of tensor products of modules.Additionally,we give another generalization of result of Xi(2012)in terms of Chevalley-Eilenberg complex.

Cylinder Coalgebras and Cylinder Coproducts for Quasitriangular Hopf Algebras

This paper introduces the concepts of cylinder coalgebras and cylinder coproducts for quasitriangular bialgebras, and points out that there exists an anti-coalgebra isomorphism （H,△^-）≌ （H,△^-）, where （H, △^-） is the cylinder coproduct, and （H,△^-） is the braided coproduct given by Kass. For any finite dimensional Hopf algebra H, the Drinfel＇d double （D（H）,△^-D（H）） is proved to be the cylinder coproduct. Let （H, H, R） be copaired Hopf algebras. If R ∈ Z（H×H） with inverse R-1 and skew inverse R, then the twisted coalgebra （H^R）^R-1 is constructed via twice twists, whose comultiplication is exactly the cylinder coproduct. Moreover, for any generalized Long dimodule, some solutions for Yang-Baxter equations, four braid pairs and Long equations are constructed via cylinder twists.

The Algebraic Properties of a Type of Infinite Lower Triangular Matrices Related to Derivatives

In this paper, Jabotinsky matrices in [4, 5] are modified and a type of infinite lower triangular matrices T(f) is discussed. Some algebraic properties of T(f) are obtained and proved. Additionally, some inverse pairs and combinatorial identities associated with derivatives are obtained.

Lie Bialgebras of Generalized Loop Virasoro Algebras

The first cohomology group of generalized loop Virasoro algebras with coefficients in the tensor product of its adjoint module is shown to be trivial. The result is used to prove that Lie bialgebra structures on generalized loop Virasoro algebras are coboundary triangular. The authors generalize the results to generalized map Virasoro algebras.

Lie Bialgebras of a Family of Lie Algebras of Block Type

Lie bialgebra structures on a family of Lie algebras of Block type are shown to be triangular coboundary.

Lie Triple Derivations of the Lie Algebra of Dominant Block Upper Triangular Matrices

Let N be the Lie algebra of all n x n dominant block upper triangular matrices over a field F. In this paper, we explicitly describe all Lie triple derivations of N when char（F） ≠ 2. As an application, we characterize Lie derivations of N when char（F） ≠ 2.