In this article,we introduce and study the class of approximately Artinian(Noetherian)C^(*)-algebras,called AR-algebras(AN-algebras),which is a simultaneous generalization of Artinian(Noetherian)C*-algebras and AF-alg...In this article,we introduce and study the class of approximately Artinian(Noetherian)C^(*)-algebras,called AR-algebras(AN-algebras),which is a simultaneous generalization of Artinian(Noetherian)C*-algebras and AF-algebras.We study properties such as the ideal property and topological dimension zero for them.In particular,we show that a faithful AR or AN algebra is strongly purely infinite iff it is purely infinite iff it is weakly purely infinite.This extends the Kirchberg's O_(∞)-absorption theorem,and implies that a weakly purely infinite C^(*)-algebra is Noetherian iff every its ideal has a full projection.展开更多
In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that thes...In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C＊-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C＊-algebra with a faithful conditional expectation.展开更多
We calculate the enveloping Lie algebras of Leibniz algebras of dimensions two and three. We show how these Lie algebras could be used to distinguish non-isomorphic (nilpotent) Leibniz algebras of low dimension in som...We calculate the enveloping Lie algebras of Leibniz algebras of dimensions two and three. We show how these Lie algebras could be used to distinguish non-isomorphic (nilpotent) Leibniz algebras of low dimension in some cases. These results could be used to associate geometric objects (loop spaces) to low dimensional Leibniz algebras.展开更多
基金supported by grants from INSF(98029498,99013953)partly supported by a grant from IPM(96430215)。
文摘In this article,we introduce and study the class of approximately Artinian(Noetherian)C^(*)-algebras,called AR-algebras(AN-algebras),which is a simultaneous generalization of Artinian(Noetherian)C*-algebras and AF-algebras.We study properties such as the ideal property and topological dimension zero for them.In particular,we show that a faithful AR or AN algebra is strongly purely infinite iff it is purely infinite iff it is weakly purely infinite.This extends the Kirchberg's O_(∞)-absorption theorem,and implies that a weakly purely infinite C^(*)-algebra is Noetherian iff every its ideal has a full projection.
文摘In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C＊-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C＊-algebra with a faithful conditional expectation.
文摘We calculate the enveloping Lie algebras of Leibniz algebras of dimensions two and three. We show how these Lie algebras could be used to distinguish non-isomorphic (nilpotent) Leibniz algebras of low dimension in some cases. These results could be used to associate geometric objects (loop spaces) to low dimensional Leibniz algebras.
