Weakly algebraic ideal topology of effect algebras

In this paper, we show that every weakly algebraic ideal of an effect algebra E induces a uniform topology(weakly algebraic ideal topology, for short) with which E is a first-countable,zero-dimensional, disconnected, locally compact and completely regular topological space, and the operation ⊕ of effect algebras is continuous with respect to these topologies. In addition, we prove that the operation of effect algebras and the operations ∧ and ∨ of lattice effect algebras are continuous with respect to the weakly algebraic ideal topology generated by a Riesz ideal.     

On Strong Kadison–Singer Algebras

We show that many Kadison–Singer algebras are maximal triangular in all algebras containing them although their definition requires the maximality taken in the class of reflexive algebras. Diagonal-trivial maximal non self-adjoint subalgebras of matrix algebras with lower dimensions are classified.     

三角Banach代数的等距同构

Let (X) and (X) be Banach algebras.Let (X) be a Banach (X),(X)-module with bounded 1.Then (X) is a Banach algebra with the usual operations and the norm ‖［AOMB］‖=‖A‖+‖M‖+‖B‖.Such an algebra is called a triangular Banach algebra.In this paper the isometric isomorphisms of triangular Banach algebras are characterized.     

具有弱$s$-置换嵌入子群的有限群

Let P be a Sylow p-subgroup of a group G with the smallest generator number d,where p is a prime.Denote by M_d(P) = {P_1,P_(2,...,)P_d} a set of maximal subgroups of P such that φ(P) = ∩_(n=1)~dP_n.In this paper,we investigate the structure of a finite group G under the assumption that the maximal subgroups in M_d(P) are weakly s-permutably embedded in G,some interesting results are obtained which generalize some recent results.Finally,we give some further results in terms of weakly s-permutably embedded subgroups.     

本刊英文版Vol.29(2013),No.12论文摘要(英文)

<正>On Strong Kadison-Singer Algebras Ai Ju DONG Dong WANG Abstract We show that many Kadison-Singer algebras are maximal triangular in all algebras containing them although their definition requires the maximality taken in the class of reflexive algebras.Diagonal-trivial maximal non self-adjoint subalgebras of matrix algebras with lower dimensions are classified.     

分裂的正则Hom-Poisson 着色代数结构

We introduce the class of split regular Hom-Poisson color algebras as the natural generalization of split regular Hom-Poisson algebras and the one of split regular Hom-Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show∑that such a split regular Hom-Poisson color algebras A is of the form A = U +αIα with U a subspace of a maximal abelian subalgebra H and any Iα, a well described ideal of A, satisfying[Iα, Iβ] + IαIβ = 0 if [α]≠[β]. Under certain conditions, in the case of A being of maximal length, the simplicity of the algebra is characterized.     

The varieties of Heisenberg vertex operator algebras

For a vertex operator algebra V with conformal vector ω,we consider a class of vertex operator subalgebras and their conformal vectors.They are called semi-conformal vertex operator subalgebras and semiconformal vectors of(V,ω),respectively,and were used to study duality theory of vertex operator algebras via coset constructions.Using these objects attached to(V,ω),we shall understand the structure of the vertex operator algebra(V,ω).At first,we define the set Sc(V,ω)of semi-conformal vectors of V, then we prove that Sc(V,ω)is an affine algebraic variety with a partial ordering and an involution map.Corresponding to each semi-conformal vector,there is a unique maximal semi-conformal vertex operator subalgebra containing it.The properties of these subalgebras are invariants of vertex operator algebras.As an example,we describe the corresponding varieties of semi-conformal vectors for Heisenberg vertex operator algebras.As an application,we give two characterizations of Heisenberg vertex operator algebras using the properties of these varieties.     

(f,ω)-Compatible Pair (B,H) for ω-Smash Coproduct Hopf Algebras

In this paper we introduce the notion of (f,ω)-compatible pair (B,H), by which we construct a Hopf algebra in the category HHYD of Yetter-Drinfeld H-modules by twisting the comultiplication of B. We also study the property of ω-smash coproduct Hopf algebras Bω H.     

The Existence of Maximal w^＊-closed Submodules in Nest Algebra Modules

Using the technique of annihilators, we characterize the w^＊-closure of the finite-partition submodule R（N, ～） of a weakly closed nest algebra module U completely; and by virtue of this characterization, we obtain a sufficient and necessary condition for U to have a maximal w^＊-closed submodule.     

ISOMETRIC ISOMORPHISMS OF TRIANGULAR BANACH ALGEBRAS

§ 1　 IntroductionLet Aand Bbe Banach algebras.Let Mbe a Banach A,B-module with bounded1 .Thatis,‖AMB‖≤‖A‖‖M‖‖B‖ for each A∈A,B∈Band M∈M.ThenT=A M0 B=A M0 B :A∈ A,B∈ B,M∈ Mis a Banach algebra with the usual operations and the normA M0 B =‖ A‖ ‖ M‖ ‖ B‖ .We call such an algebra a triangular Banach algebra.In[1 ] ,the derivation of triangular Ba-nach algebras is studied and the firstcohomology groups ofsome special triangular Banachalgebras are explicitl…