A specialization of prinjective Ringel-Hall algebra and the associated Lie algebra

In the present paper we describe a specialization of prinjective Ringel-Hall algebra to 1, for prinjective modules over incidence algebras of posets of finite prinjective type, by generators and relations. This gives us a generalisation of Serre relations for semisimple Lie algebras. Connections of prinjective Ringel-Hall algebras with classical Lie algebras are also discussed.     

ON Δ-GOOD MODULE CATEGORIES OF QUASI-HEREDITARY ALGEBRAS

A useful reduction is presented to determine the finiteness of △-good module category F(△)of a quasi-heredltary algebra. As an application of the reduction, the f(△)-finitenetess of quasi-hereditary M-twisted double incidence algebras of posets is discussed. In particular, a complete classification of F(△)-finite M-twisted double incidence algebras is given in case the posets are linearly ordered.     

PropertyΠ_σand tensor products of operator algebras

In this paper,we introduce PropertyΠ_σof operator algebras and prove that nest sub- algebras and the finite-width CSL subalgebras of arbitrary von Neumann algebras have PropertyΠ_σ. Finally,we show that the tensor product formula alg_ML_1(?)alg_NL_2=alg_(M(?)N)(L_1(?)L_2) holds for any two finite-width CSLs L_1 and L_2 in arbitrary von Neumann algebras M and N,respectively.     

效应代数上的态射性质

In the present paper the properties of morphisms in effect algebras are discussed. The conditions for the morphisms in effect algebras to be join-preservation and meet-preservation are given. From the categorical point of view, some properties of ideals, filters and congruence relations under morphisms are obtained.     

States on sharply dominating effect algebras

We prove that sharply dominating Archimedean atomic lattice effect algebras can be characterized by the property called basic decomposition of elements.As an application we prove the state smearing theorem for these effect algebras.     

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.     

Property ∏σ and tensor products of operator algebras

In this paper, we introduce Property ∏σ of operator algebras and prove that nest subalgebras and the finite-width CSL subalgebras of arbitrary von Neumann algebras have Property ∏σ.Finally, we show that the tensor product formula alg ML1-(×)algNL2 = algM-(×)N(L1 (×) L2) holds for any two finite-width CSLs L1 and L2 in arbitrary von Neumann algebras M and N, respectively.     

本刊英文版2023年66卷第5期(887–1140)摘要（英文）

<正>Growth of generalized Weyl algebras over polynomial algebras and Laurent polynomial algebras Xiangui Zhao Abstract We study the growth and the Gelfand-Kirillov dimension(GK-dimension) of the generalized Weyl algebra(GWA) A = D(σ, a), where D is a polynomial algebra or a Laurent polynomial algebra. Several necessary and sufficient conditions for GKdim(A) = GKdim(D) + 1 are given.     

Purely Hom-Lie bialgebras

In this paper, we first show that there is a Hom-Lie algebra structure on the set of(σ, σ)-derivations of an associative algebra. Then we construct the dual representation of a representation of a Hom-Lie algebra.We introduce the notions of a Manin triple for Hom-Lie algebras and a purely Hom-Lie bialgebra. Using the coadjoint representation, we show that there is a one-to-one correspondence between Manin triples for Hom-Lie algebras and purely Hom-Lie bialgebras. Finally, we study coboundary purely Hom-Lie bialgebras and construct solutions of the classical Hom-Yang-Baxter equations in some special Hom-Lie algebras using Hom-O-operators.     

Hypercontinuous Posets

The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent:(1) P is hypercontinuous;(2) the dual of P is generalized completely continuous;(3) the normal completion of P is a hypercontinuous lattice. In addition, the relational representation and the intrinsic characterization of hypercontinuous posets are obtained.