离散群上的Toeplitz算子代数的顺从性

设(G,G )为一个拟格序群,H为G 的一个可传、定向子集．记GH=G .H-1, 令TGH为相应的Toeplitz算子代数．利用G 的等距协变表示刻画了(G,GH)的顺从性。当 G=G .G -1时,证明了(G,GH)为顺从当且仅当G为顺从．     

离散群上的Toeplitz算子

本文通过在一般的离散群上引进有限提升集、全有限提升集，在广泛的情形下，刻划了广义Ｈａｒｄｙ空间上Ｔｏｅｐｌｉｔｚ算子的一些性质     

群的形变收缩及Toeplitz代数

设G为一个离散群,(G,G_ )为一个拟偏序群使得G_ ~0=G_ ∩G_ ~(-1)为G的非平凡子群。令[G]为G关于G_ ~0的左倍集全体,|G_ |为[G]的正部。记T~(G_ )和T~([G_ ])为相应的Toeplitz代数。当存在一个从G到G_ ~0上的形变收缩映照时,我们证明了T~(G_ )酉同构于T~([G_ ])×C_r~*(G_ ~0)的一个C_-~*c子代数。若进一步,G_ ~0还为G的一个正规子群,则T~(G_ )与T~([G_ ])×C_r~*(G_ ~0)酉同构。     

Toeplitz代数的上同调群

本文计算了Hardy空间上符号在H∞或C以及H∞＋C中的Toenlitz代数的上同调群．其结果说明,C*-代数的上同调群比VonNeumann代数的上同调群复杂．     

离散交换群上Toeplitz 算子的代数性质

广泛的意义下定义 Toeplitz 算子, 给出了Toeplitz 算子乘积仍为Toeplitz 算子的充分必要条件, Toeplitz算子是正规算子的充分必要条件以及 Toeplitz 算子可交换的一个必要条件,从而推广了经典 Toeplitz 算子的相应结果.     

Twisted Semigroup Crossed Products and Twisted Toeplitz Algebras of Ordered Groups

Let г^＋ be the positive cone of a totally ordered abelian group г, and σa cocycle in г. We study the twisted crossed products by actions of г＋ as endomorphisms of C^＊-algebras, and use this to generalize the theorem of Ji.     

The Ideal Structure of Toeplitz Algebras

We investigate the ideal structure of the Toeplitz algebra of a totally ordered abelian group . We show that the primitive ideals of are parametrised by the disjoint union of the duals of the order ideals of , and identify the hull-kernel topology on when the chain of orderideals in is isomorphic to a subset of      

Toeplitz Algebras on Dirichlet Spaces

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＬｅｔＢｎｂｅｔｈｅｕｎｉｔｂａｌｌｉｎＣｎ,ａｎｄｄｖｔｈｅｎｏｒｍａｌｉｚｅｄＬｅｂｅｓｇｕｅｍｅａｓｕｒｅｏｎＢｎ.ＳｏｂｏｌｅｖｓｐａｃｅＬ2 ,1ｉｓｔｈｅｓｐａｃｅｏｆｆｕｎｃｔｉｏｎｓｕ :Ｂｎ→Ｃ ,ｆｏｒｗｈｉｃｈｔｈｅｎｏｒｍ‖ｕ‖1/ 2 =∑ｎｉ=1 ∫Ｂｎ ｕ ｚｉ(ｚ) 2 + ｕ ｚｉ(ｚ) 2 ｄν1/ 2 <∞ .Ｌ2 ,1/ 2 ｉｓａＨｉｌｂｅｒｔｓｐａｃｅｗｉｔｈｔｈｅｉｎｎｅｒｐｒｏｄｕｃｔ〈ｕ ,ｖ〉1/ 2 =∑ｎｉ=1〈 ｕ ｚｉ, ｕ ｚｉ〉Ｌ2 (ｄν) +∑ｎｉ=1〈 ｕ ｚｉ, ｕ …     

Embedding Properties of Metabelian Lie Algebras and Metabelian Discrete Groups

We show that for every natural number m a finitely generatedmetabelian group G embeds in a quotient of a metabelian groupof type FP_m. Furthermore, if m 4, the group G can be embeddedin a metabelian group of type FP_m. For L a finitely generatedmetabelian Lie algebra over a field K and a natural number mwe show that, provided the characteristic p of K is 0 or p >m, then L can be embedded in a metabelian Lie algebra of typeFP_m. This result is the best possible as for 0 < p m everymetabelian Lie algebra over K of type FP_m is finite dimensionalas a vector space.     

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.     

The Groups LS and Morphisms of Quadratic Extensions

For a morphism of quadratic extensions of antistructures, groups similar to the groups of obstructions to splitting along one-sided submanifolds are defined. These groups are a natural generalization of the splitting obstruction groups. The results obtained open additional possibilities for constructing groups and natural maps in L-theory.     

Covering Morphisms in Categories of Relational Algebras

In this paper we use Janelidze’s approach to the classical theory of topological coverings via categorical Galois theory to study coverings in categories of relational algebras. Moreover, we present characterizations of effective descent morphisms in the categories of M-ordered sets and of multi-ordered sets.     

Toeplitz算子代数的归纳极限

设(G_1,E_1),(G_2,E_2)为两个拟格序群,记■~(E_1),■~(E_2)为相应的Toeplitz算子代数．设■：G_1→G_2为一个保单位的群同态,使得■(E_1)■E_2．本文给出了上述两个Toeplitz算子代数间的自然同态映照成为C~*-代数的单同态的充要条件,刻画了Toeplitz算子代数的归纳极限,证明了任何自由群上的Toeplitz算子代数是顺从的．     

Toeplitz Operators and Algebras on Dirichlet Spaces

ＬｅｔＤｂｅｔｈｅｕｎｉｔｄｉｓｋｉｎｔｈｅｃｏｍｐｌｅｘｐｌａｎｅＣ,ａｎｄｄＡ（ｚ）＝１πｄｘｄｙｔｈｅｎｏｒｍａｌｉｚｅｄＬｅｂｅｓｇｕｅｍｅａｓｕｒｅｏｎＤ．ＴｈｅＳｏｂｏｌｅｖｓｐａｃｅＬ２,１ｉｓｄｅｆｉｎｅｄｔｏｂｅｔｈｅｃｏｌｅｃｔｉ...     

Effective Descent Morphisms in Categories of Lax Algebras

In this paper we investigate effective descent morphisms in categories of reflexive and transitive lax algebras. We show in particular that open and proper maps are of effective descent, result that extends the corresponding results for the category of topological spaces and continuous maps.     

Realising Smashing Localisations as Morphisms of DG Algebras

For a smashing localisation L of the derived category of a differential graded (dg) algebra A we construct a dg algebra A _L and a morphism of dg algebras A→A _L that induces the canonical map in cohomology. As a first application we obtain a localisations of a dg algebra A with graded commutative homology at a prime ideal in the homology H ^* A, namely a morphism of dg algebras. As a second application we can use results of Keller to “model” every smashing localisation of compactly generated algebraic triangulated categories by a morphism of dg algebras.      

Irreducible Morphisms Between Modules over a Repetitive Algebras

We describe the irreducible morphisms in the category of modules over a repetitive algebra. We find three special canonical forms: The first canonical form happens when all the component morphisms are split monomorphisms, the second when all the component morphisms are split epimorphisms and the third when there is exactly one irreducible component map. Also, we obtain the same result for the irreducible homomorphisms in the stable category of modules over a repetitive algebra.     

Discrete Koszul Algebras

Discrete Koszul algebra, another extension of Koszul algebras, is introduced in this paper. The Yoneda algebra of a discrete Koszul algebra is investigated in detail. As an application, we give an answer to a question proposed by Green and Marcos (Commun Algebra 33:1753–1764, 2005). In particular, the relationship between discrete Koszul algebras and Koszul algebras is established. Further, we construct new discrete Koszul algebras from the given ones in terms of one-point extension.     

Effective Codescent Morphisms in Some Varieties of Universal Algebras

The paper gives a sufficient condition formulated in a syntactical form for all codescent morphisms of a variety of universal algebras satisfying the amalgamation property to be effective. This result is further used in proving that all codescent morphisms of (left/right-)quasigroups, loops, and magmas are effective.