On Unital Full Amalgamated Free Products of Quasidiagonal C*-Algebras

In the paper, we consider the question as to whether a unital full amalgamated free product of quasidiagonal C*-algebras is itself quasidiagonal. We give a sufficient condition for a unital full amalgamated free product of quasidiagonal C*-algebras with amalgamation over a finite-dimensional C*-algebra to be quasidiagonal. By applying this result, we conclude that the unital full free product of two AF algebras with amalgamation over a finite-dimensional C*-algebra is AF if there exists a faithful tracial state on each of the two AF algebras such that the restrictions of these states to the common subalgebra coincide.     

Congruence Permutable Symmetric Extended de Morgan Algebras

An algebra A is said to be congruence permutable if any two congruences on it are permutable. This property has been investigated in several varieties of algebras, for example, de Morgan algebras, p-algebras, Kn,0-algebras. In this paper, we study the class of symmetric extended de Morgan algebras that are congruence permutable. In particular we consider the case where A is finite, and show that A is congruence permutable if and only if it is isomorphic to a direct product of finitely many simple algebras.     

Characterizations of algebras with small homological dimensions

We introduce the class of double tilted algebras, containing the class of tilted algebras and prove various characterizations. In particular, we show that the class of double tilted algebras is the class of all artin algebras whose AR-quiver admits a faithful double section with a natural property. Moreover, we prove that the class of double tilted algebras coincides with the class of all artin algebras of global dimension three, for which every indecomposable finitely generated module has projective or injective dimension at most one. We also describe the structure of the category of finitely generated modules as well as the AR-quiver of double tilted algebras.     

SVEP for multipliers on a faithful commutative Banach algebra

We give some sufficient conditions that each multiplier on a faithful commutative Banach algebra has SVEP. On the other hand, we show that there exist a faithful commutative Banach algebra and a multiplier on it without SVEP. Such examples of multipliers can actually be found within the class of multiplication operators on unital commutative Banach algebras. This answers in negative a question that is stated as Open problem 6.2.1 by Laursen and Neumann, 2000.

     

Conformal representations of Leibniz algebras

We study the embedding construction of Lie dialgebras (Leibniz algebras) into conformal algebras. This construction leads to the concept of a conformal representation of Leibniz algebras. We prove that each (finite-dimensional) Leibniz algebra possesses a faithful linear representation (of finite type). As a corollary we give a new proof of the Poincaré-Birkhoff-Witt theorem for Leibniz algebras.     

广义分段Koszul代数

广义分段Koszul代数(简称为K_p代数)一般是一类二次代数,其平凡模允许有非单纯的投射分解.利用Yoneda-Ext代数E(A)给出了分次代数A是K_p代数的一个充分条件,同时讨论了K_p代数的商代数是否继承K_p性质.     

广义分段Koszul代数

广义分段Koszul代数(简称为κ_p代数)一般是一类二次代数,其平凡模允许有非单纯的投射分解.利用Yoneda-Ext代数E(A)给出了分次代数A是κ_p代数的一个充分条件,同时讨论了κ_p代数的商代数是否继承κ_p性质.     

n‐linear weakly Heyting algebras

The present paper introduces and studies the variety ????_n of n‐linear weakly Heyting algebras. It corresponds to the algebraic semantic of the strict implication fragment of the normal modal logic K with a generalization of the axiom that defines the linear intuitionistic logic or Dummett logic. Special attention is given to the variety ????₂ that generalizes the linear Heyting algebras studied in [10] and [12], and the linear Basic algebras introduced in [2]. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The class of polyadic algebras has the super amalgamation property

We show that for infinite ordinals α the class of polyadic algebras of dimension α has the super amalgamation property (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Graded extended Lie-type algebras

The class of extended Lie-type algebras contains the ones of associative algebras, Lie algebras, Leibniz algebras, dual Leibniz algebras, pre-Lie algebras, and Lie-type algebras, etc. We focus on the class of extended Lie-type algebras graded by an Abelian group G and study its structure, by stating, under certain conditions, a second Wedderburn-type theorem for this class of algebras.     

On a property ofL p spaces on semifinite von Neumann algebras

A characterization of the traces in a broad class of weights on von Neumann algebras is obtained. A new property of the domain ideals of these traces is proved. In the semifinite case, a relation for a faithful normal trace is established. This result is new even for the algebra of all bounded operators on a Hilbert space. Applications of the main result to the structure theory of von Neumann algebras and to the Köthe duality theory for ideal spaces of Segal measurable operators are given.Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 185–190, August, 1998.The author wishes to express his deep gratitude to Professor A. N. Sherstnev for setting the problem and for fruitful discussions.This research was supported by the Russian Foundation for Basic Research under grant No. 95-01-00025.     

Initial Chain Algebras on Pseudotrees

We investigate a new class of Boolean algebra, called initial chain algebras on pseudotrees. We discuss the relationship between this class and other classes of Boolean algebras. Every interval algebra, and hence every countable Boolean algebra, is an initial chain algebra. Every initial chain algebra on a tree is a superatomic Boolean algebra, and every initial chain algebra on a pseudotree is a minimally-generated Boolean algebra.We show that a free product of two infinite Boolean algebras is an initial chain algebra if and only if both factors are countable.     

INVARIANTS UNDER STABLE EQUIVALENCES OF MORITA TYPE

The aim of this article is to study some invariants of associative algebras under stable equivalences of Morita type.First of all,we show that,if two finite-dimensional selfinjective k-algebras are sta...     

Derivations of noncommutative Arens algebras

The present paper deals with derivations of noncommutative Arens algebras. We prove that every derivation of an Arens algebra associated with a von Neumann algebra and a faithful normal finite trace is inner. In particular, each derivation on such algebras is automatically continuous in the natural topology, and in the commutative case, even for semi-finite traces, all derivations are identically zero. At the same time, the existence of noninner derivations is proved for noncommutative Arens algebras with a semi-finite but nonfinite trace.     

Confluent operator algebras and the closability property

Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the transitive algebra problem. More precisely, if A is a two-transitive algebra with the closability property, then A is dense in the algebra of all bounded operators, in the weak operator topology. In this paper we focus on algebras generated by a completely nonunitary contraction, and produce several new classes of algebras with the closability property. We show that this property follows from a certain strict cyclicity property, and we give very detailed information on the class of completely nonunitary contractions satisfying this property, as well as a stronger property which we call confluence.     

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.     

The Endomorphism Kernel Property in Finite Distributive Lattices and de Morgan Algebras

Abstract

An algebra 𝒜 has the endomorphism kernel property if every congruence on 𝒜 different from the universal congruence is the kernel of an endomorphism on 𝒜. We first consider this property when 𝒜 is a finite distributive lattice, and show that it holds if and only if 𝒜 is a cartesian product of chains. We then consider the case where 𝒜 is an Ockham algebra, and describe in particular the structure of the finite de Morgan algebras that have this property.     

Automorphisms of Generalized Down-Up Algebras

A generalization of down-up algebras was introduced by Cassidy and Shelton (2004 Cassidy , T. , Shelton , B. ( 2004 ). Basic properties of generalized down-up algebras . J. Algebra 279 ( 1 ): 402 – 421 .[Crossref], [Web of Science ®] , [Google Scholar]), the so-called “generalized down-up algebras”. We describe the automorphism group of conformal Noetherian generalized down-up algebras L(f, r, s, γ) such that r is not a root of unity, listing explicitly the elements of the group. In the last section, we apply these results to Noetherian down-up algebras, thus obtaining a characterization of the automorphism group of Noetherian down-up algebras A(α, β, γ) for which the roots of the polynomial X ² ? α X ? β are not both roots of unity.