TWISTED PRODUCTS AND SMASH PRODUCTS OVER WEAK HOPF ALGEBRAS

This paper gives a sufficient and necessary condition for twisted products to be weak Hopf algebras, moreover, gives a description for smash products to be weak Hopf algebras. It respectively generalizes R.K.Molnar's major result and I.Boca's result.

MAPS PRESERVING STRONG SKEW LIE PRODUCT ON FACTOR VON NEUMANN ALGEBRAS

Let A be a factor von Neumann algebra and Ф be a nonlinear surjective map from A onto itself. We prove that, if Ф satisfies that Ф（A）Ф（B） - Ф（B）Ф（A）＊ -- AB - BA＊ for all A, B ∈ A, then there exist a linear bijective map ψA →A satisfying ψ（A）ψ（B） - ψ（B）ψ（A）＊ = AB - BA＊ for A, B ∈ A and a real functional h on A with h（0） -= 0 such that Ф（A） = ψ（A） ＋ h（A）I for every A ∈ A. In particular, if .4 is a type I factor, then, Ф（A） = cA ＋ h（A）I for every A ∈ .4, where c = ±1.

On the Product and Factorization of Lattice Implication Algebras

In this paper,the concepts of product and factorization of lattice implication algebra are proposed,the relation between lattice implication product algebra and its factors and some properties of lattice implication product algebras are discussed.

Research on Production Process Control Method Combined Stochastic Process Algebra and Stochastic Petri Nets

A hierarchical closed-loop production control scheme integrating scheduling,control and performance evaluation is discussed.Firstly,the production process is divided into two main hierarchies:the lower level is the physical operation level and the upper one is the management level.Secondly,the schedule template for the management level and the activity template for the physical operation level are constructed separately,the tasks in the schedule have the ability to make partial decisions,and the per- formance parameters are introduced into activity template.Thirdly,the two levels use different model representations:stochastic process algebra for the management level whose output is the control commands and stochastic Petri net for the physical operation lev- el which is the execution of the control commands.Then,the integration of the two levels is the control commands mapping into the lower physical operations and the responses feeding back to the upper decision-making that are defined by some transition functions. Under the proposed scheme,the production process control of a flexible assembly is exemplified.It is concluded that the process con- trol model has partial ability to make decision on-line for uncertain and dynamic environments and facilitates reasoning about the be- haviors of the process control,and performance evaluation can be done online for real-time scheduling to ensure the global optimiza- tion.

Hopf Algebra of Labeled Simple Graphs

A lot of combinatorial objects have a natural bialgebra structure. In this paper, we prove that the vector space spanned by labeled simple graphs is a bialgebra with the conjunction product and the unshuffle coproduct. In fact, it is a Hopf algebra since it is graded connected. The main conclusions are that the vector space spanned by labeled simple graphs arising from the unshuffle coproduct is a Hopf algebra and that there is a Hopf homomorphism from permutations to label simple graphs.

Super-Shuffle Product and Cut-Box Coproduct on (0,1)-Matrices

In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple graphs. In this paper, we generalize the super-shuffle product and the cut-box coproduct from labeled simple graphs to (0,1)-matrices. Then we prove that the vector space spanned by (0,1)-matrices with the super-shuffle product is a graded algebra and with the cut-box coproduct is a graded coalgebra.

基于外积求解颗粒平衡问题

提出一种简洁有效的基于外积的方法,对无摩擦的二维圆盘、二维凸颗粒以及三维球体的力学平衡方程进行求解和分析。理论结果表明,圆盘与球体上输出力的大小与输入力的大小成正比,因此引入了力传递的概念,并且导出力传递系数与接触结构的关系。对于凸颗粒,导出了输出力大小与输入力以及力矩的关系式。在已知圆盘上的平均正压力时,导出了各个接触力大小的公式并给出其几何意义。文中提出的方法以及计算的结果,对于求解其他物理问题中的向量方程有意义,对于进一步研究力学网络上的平衡方程有重要价值。

高等代数荣誉课程教学:理论挂帅,软硬并举,实现四化

高等代数荣誉课程的教学目标是现代化,国际化,代数化和算法化.

CROSSED PRODUCTS BY FINITE GROUP ACTIONS WITH CERTAIN TRACIAL ROKHLIN PROPERTY

We introduce a special tracial Rokhlin property for unital C~＊-algebras. Let A be a unital tracial rank zero C~＊-algebra（or tracial rank no more than one C~＊-algebra）. Suppose that α ： G → Aut（A） is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~＊-algebra. Then, the crossed product C~＊-algebra C~＊（G, A, α） has tracia rank zero（or has tracial rank no more than one）. In fact,we get a more general results.

THE UNIVERSAL DUAL COMODULE OF MODULE IN HOPF ALGEBRAS

The purpose of this paper is to present some dual properties of dual comodule. It turns out that dual comodule has universal property (cf.Theorem 2). Since (( )*,()°) is an adjoint pair (cf.Theorem 3), some nice properties of functor ( )° are obtained. Finally Theoram 4 provides that the cotensor product is the dual of the tensor product by (M (?)A N)°≌M°□A°N°. Moreover, the result Hom(M,JV)≌ComA°(N°,M°) is proved for finite related modules M, N over a reflexive algebra A.

APPROXIMATION OF ADJOINT OF A MULTIPLIER ON BANACH ALGEBRAS

For a Banach algebra A, we denote by .A＊ and .A＊＊ the first and the second duals of A respectively. Let T be a mapping from .A＊ to itself. In this article, we will investigate some stability results concerning the equations T（αf ＋ βg） -= αT（f） ＋ βT（g）, T（af） = aT（f） andT（αf ＋βg） ＋ T（αf - βg） =- 2α2T（f） ＋ 2β2T（g） where f, g e .A＊, a ∈ A, and α,β ∈ Q ／ {0}.

Global dimension of weak smash product

In Artin algebra representation theory there is an important result which states that when the order of G is invertible in Λ then gl.dim(ΛG)=gl.dim(Λ). With the development of Hopf algebra theory, this result is generalized to smash product algebra. As known, weak Hopf algebra is an important generalization of Hopf algebra. In this paper we give the more general result, that is the relation of homological dimension between an algebra A and weak smash product algebra A#H, where H is a finite dimensional weak Hopf algebra over a field k and A is an H-module algebra.

Random quadralinear forms and schur product on tensors

In this work, we made progress on the problem that rpqlll哪(( is a Banach algebra under schur product. Our results extend Tonges results. We also obtained estimates for the norm of the random quadralinear form A: MNKHrpqsllll创串C, defined by: A(ei, ej, ek, es)=ijksa, where the (aijks)s are uniformly bounded, independent, mean zero random variables. We proved that under some conditions rpqsllll哪?(( is not a Banach algebra under schur product.

A Characterization of Jacobson Radical in Γ-Banach Algebras

Let V1 and V2 be two -Banach algebras and Ri be the right operator Banach algebra and Li be the left operator Banach algebra of Vi(i=1,2). We give a characterization of the Jacobson radical for the projective tensor product V1rV2 in terms of the Jacobson radical for R1rL2. If V1 and V2 are isomorphic, then we show that this characterization can also be given in terms of the Jacobson radical for R2rL1.

Duality theorem for weak L-R smash products

This paper gives a duality theorem for weak L-R smash products, which extends the duality theorem for weak smash products given by Nikshych.

GENERALIZED DERIVATIONS ON PARABOLIC SUBALGEBRAS OF GENERAL LINEAR LIE ALGEBRAS

Let P be a parabolic subalgebra of a general linear Lie algebra gl（n,F） over a field F, where n ≥ 3, F contains at least n different elements, and char（F） ≠ 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.

A Local Characterization of Lie Homomorphisms of Nest Algebras

In this paper,linear maps preserving Lie products at zero points on nest algebras are studied.It is proved that every linear map preserving Lie products at zero points on any finite nest algebra is a Lie homomorphism.As an application,the form of a linear bijection preserving Lie products at zero points between two finite nest algebras is obtained.

MAURER-CARTAN EQUATION OF A_∞-ALGEBRAS

The axioms of A ∞ algebras can be written as Maurer Cartan equation.Infi nitesimal multiplication of a graded associative algebra is defined and the integrability of infinitesimal multiplication is discussed through the Massey F product.

H-separable Hopf Galois Extensions and Azumaya Algebra

Let H be a finite dimensional semisimple Hopf algebra over a field and A an H-module algebra. In this paper, we characterize any H-separable Galois extension of an Azumaya algebra. Assuming that A/AH is an H-separable extension, we prove that A/AH is H-Galois and AH is Azumaya if and only if A#H is an Azumaya Z-algebra, where Z is the center of A#H(not necessarily C(A)H).