The authors prove that the crossed product of an infinite dimensional simple separable unital C*-algebra with stable rank one by an action of a finite group with the tracial Rokhlin property has again stable rank one....The authors prove that the crossed product of an infinite dimensional simple separable unital C*-algebra with stable rank one by an action of a finite group with the tracial Rokhlin property has again stable rank one. It is also proved that the crossed product of an infinite dimensional simple separable unital C*-algebra with real rank zero by an action of a finite group with the tracial Rokhlin property has again real rank zero.展开更多
Let A be a unital simple C-algebra of real rank zero,stable rank one,with weakly unperforated K<sub>0</sub>（A）and unique normalized quasi-trace τ,and let X be a compact metric space.We show that two mon...Let A be a unital simple C-algebra of real rank zero,stable rank one,with weakly unperforated K<sub>0</sub>（A）and unique normalized quasi-trace τ,and let X be a compact metric space.We show that two monomorphisms Φ,Ψ:C（X）→A are approximately unitarily equivalent if and only if Φ and Ψ induce the same element in KL（C（X）,A）and the two linear functionals τ ο Φ and τ ο Φ are equal.We also show that,with an injectivity condition,an almost multiplicative morphism from C（X） into A with vanishing KK-obstacle is close to a homomorphism.展开更多
Let A and B be C^＊-algebras. An extension of B by A is a short exact sequence O→A→E→B→O. （＊） Suppose that A is an AT-algebra with real rank zero and B is any AT-algebra. We prove that E is an AT-algebra if an...Let A and B be C^＊-algebras. An extension of B by A is a short exact sequence O→A→E→B→O. （＊） Suppose that A is an AT-algebra with real rank zero and B is any AT-algebra. We prove that E is an AT-algebra if and only if the extension （＊） is quasidiagonal.展开更多
This paper is a survey on the recent work of the authors and their col-laborators on the Classification of Inductive Limit C*-algebras. Some examples are presented to explain several important ideas.
基金Project supported by the National Natural Science Foundation of China (No. 10771161)
文摘The authors prove that the crossed product of an infinite dimensional simple separable unital C*-algebra with stable rank one by an action of a finite group with the tracial Rokhlin property has again stable rank one. It is also proved that the crossed product of an infinite dimensional simple separable unital C*-algebra with real rank zero by an action of a finite group with the tracial Rokhlin property has again real rank zero.
基金Research partially supported by NSF Grants DMS 93-01082(H.L)and DMS-9401515(G.G)This work was reported by the first named author at West Coast Operator Algebras Seminar(Sept.1995,Eugene,Oregon)
文摘Let A be a unital simple C-algebra of real rank zero,stable rank one,with weakly unperforated K<sub>0</sub>（A）and unique normalized quasi-trace τ,and let X be a compact metric space.We show that two monomorphisms Φ,Ψ:C（X）→A are approximately unitarily equivalent if and only if Φ and Ψ induce the same element in KL（C（X）,A）and the two linear functionals τ ο Φ and τ ο Φ are equal.We also show that,with an injectivity condition,an almost multiplicative morphism from C（X） into A with vanishing KK-obstacle is close to a homomorphism.
文摘Let A and B be C^＊-algebras. An extension of B by A is a short exact sequence O→A→E→B→O. （＊） Suppose that A is an AT-algebra with real rank zero and B is any AT-algebra. We prove that E is an AT-algebra if and only if the extension （＊） is quasidiagonal.
基金Both authors are supported by NSF grant DMS9970840 This material is also based uponwork supported by,the U.S. Army Research Office under grant number DAADl9-00-1-0152 for both authors.
文摘This paper is a survey on the recent work of the authors and their col-laborators on the Classification of Inductive Limit C*-algebras. Some examples are presented to explain several important ideas.
