1 Introduction The classification is an important subject in studying operator algebras. Many works have been done for the classification of Von Neumann algebras. In the last two decades, with the development of opera...1 Introduction The classification is an important subject in studying operator algebras. Many works have been done for the classification of Von Neumann algebras. In the last two decades, with the development of operator K-theory, more and more attention has been paid to this problem for C~*-algebras, but we have not seen any great progress for its complex展开更多
This paper gives the intrinsic character of the classification for AF-algebras defined by J.Cuntz and G. K. Pedersen in terms of their dimension groups.
This paper is a continuation of [1]. It gives some applications of the results in [1], containing some examples of pure-infinite AF-algebras and the invariant properties of the types of the C-extensions by two AF-alge...This paper is a continuation of [1]. It gives some applications of the results in [1], containing some examples of pure-infinite AF-algebras and the invariant properties of the types of the C-extensions by two AF-algebras of the same type.展开更多
We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asy...We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asymptotic direct system of finite-dimensional C^(*)-algebras.展开更多
Let A be a unital AF-algebra （simple or non-simple） and let α be an automorphism of A. Suppose that α has certain Rokhlin property and A is α-simple. Suppose also that there is an integer J ≥ 1 such that J α＊...Let A be a unital AF-algebra （simple or non-simple） and let α be an automorphism of A. Suppose that α has certain Rokhlin property and A is α-simple. Suppose also that there is an integer J ≥ 1 such that J α＊^J0 =idKo（A）. The author proves that A α Z has tracial rank zero.展开更多
文摘1 Introduction The classification is an important subject in studying operator algebras. Many works have been done for the classification of Von Neumann algebras. In the last two decades, with the development of operator K-theory, more and more attention has been paid to this problem for C~*-algebras, but we have not seen any great progress for its complex
文摘This paper gives the intrinsic character of the classification for AF-algebras defined by J.Cuntz and G. K. Pedersen in terms of their dimension groups.
文摘This paper is a continuation of [1]. It gives some applications of the results in [1], containing some examples of pure-infinite AF-algebras and the invariant properties of the types of the C-extensions by two AF-algebras of the same type.
基金Supported by Natural Science Foundation of Jiangsu Province,China (No.BK20171421)。
文摘We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asymptotic direct system of finite-dimensional C^(*)-algebras.
基金supported by the National Natural Science Foundation of China (Nos.10771069,10671068)the Shanghai Priority Academic Discipline (No.B407)
文摘Let A be a unital AF-algebra （simple or non-simple） and let α be an automorphism of A. Suppose that α has certain Rokhlin property and A is α-simple. Suppose also that there is an integer J ≥ 1 such that J α＊^J0 =idKo（A）. The author proves that A α Z has tracial rank zero.
