A characterization of the algebra <Emphasis Type="Italic">C</Emphasis><Subscript><Emphasis Type="Italic">β</Emphasis></Subscript>(Ω)

We study some properties of algebras of continuous functions on a locally compact space, these algebras being equipped with the topology defined by a family of multiplication operators (β-uniform algebras). We prove an analog of a theorem due to Sheinberg for β-uniform algebras [see Uspekhi Mat. Nauk, 32:5 (197) (1977), 203–204].     

A characteristic property of the algebra <Emphasis Type="Italic">C</Emphasis>(Ω)<Subscript><Emphasis Type="Italic">ß</Emphasis></Subscript>

We study some properties of the algebras of continuous functions on a locally compact space whose topology is defined by the family of all multiplication operators (β-uniform algebras). We introduce the notion of a β-amenable algebra and show that a β-uniform algebra is β-amenable if and only if it coincides with the algebra of bounded functions on a locally compact space (an analog of M. V. She?nberg’s theorem for uniform algebras).     

The Nilpotency Properties of the Leibniz Algebra Mn(C)D

We study the nilpotency properties of the Leibniz algebras constructed by means of D-mappings on the algebra of complex square matrices M _n (C). In particular, we obtain a criterion for nilpotency of these algebras in terms of the properties of a D-mapping. We prove also that the Leibniz algebras under consideration cannot be simple.     

Les Algebres A-F-normees Advertiblement Completes

We introduce the class ofA —F-normed algebras. It lies between that of locally bounded algebras and the one ofF*-algebras considered by W. Zelazko. We examine the structure of these algebras; and give some spectral theory results under the assumption of advertible completeness as generalized by A. Mallios.

     

Strict Topologies as Topological Algebras

Let X be a completely regular Hausdorff space, C_b(X) the space of all scalar-valued bounded continuous functions on X with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally m-convex.     

Levi--Tanaka algebras and homogeneous C R manifolds

In this paper we take up the problem of discussing C R manifolds of arbitrary C R codimension. We closely follow the general method of N.~Tanaka, while concentrating our attention to the case of manifolds endowed with partial complex structures. This study required a deeper understanding of the structure of the Levi--Tanaka algebras, which are the canonical prolongation of pseudocomplex fundamental graded Lie algebras. These algebras enjoy special properties, the understanding of which provided also a way to build up several different examples and points to a rich field of investigations. Here we restrained further our consideration to the homogeneous models.     

A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach

The aim of this paper is to classify (lócally) all torsion-less locally homogeneous affine connections on two-dimensional manifolds from a group-theoretical point of view. For this purpose, we are using the classification of all non-equivalent transitive Lie algebras of vector fields in ℝ² according to P.J. Olver [7].     

Quasi-Hereditary Extension Algebras

The paper is a continuation of the authors' study of quasi-hereditary algebras whose Yoneda extension algebras (homological duals) are quasi-hereditary. The so-called standard Koszul quasi-hereditary algebras, presented in this paper, have the property that their extension algebras are always quasi-hereditary. In the natural setting of graded Koszul algebras, the converse also holds: if the extension algebra of a graded Koszul quasi-hereditary algebra is quasi-hereditary, then the algebra must be standard Koszul. This implies that the class of graded standard Koszul quasi-hereditary algebras is closed with respect to homological duality. Another immediate consequence is the fact that all algebras corresponding to the blocks of the category O are standard Koszul.     

Order Continuity of Locally Compact Boolean Algebras

The main purpose of this paper is to exhibit the decisive role that order continuity plays in the structure of locally compact Boolean algebras as well as in that of atomic topological Boolean algebras. We prove that the following three conditions are equivalent for a topological Boolean algebra B: (1) B is compact; (2) B is locally compact, Boolean complete, order continuous; (3) B is Boolean complete, atomic and order continuous. Note that under the discrete topology any Boolean algebra is locally compact.     

标度广义效应代数和标度效应代数的结构

研究了标度广义效应代数与标度效应代数的代数结构,给出了比较完整的结果.通过引入全标度广义代数的概念,本文证明了区间[0,1)上的标度广义效应代数和单位区间[0,1]上的标度效应代数完全由单位区间上的阿基米德余模确定,标度广义效应代数恰同构于全标度广义代数的下集.若标度广义代数满足局部有限条件,则它同构于实数加法群的子群代数.满足(S)条件的标度效应代数同构于实数加法群的子群代数和全标度广义代数的字典序乘积的子代数.