A topological isomorphism invariant for certain AF algebras
نویسنده
چکیده
For certain AF algebras, a topological space is described which provides an isomorphism invariant for the algebras in this class. These AF algebras can be described in graphical terms by virtue of the existence of a certain type of Bratteli diagram, and the orderpreserving automorphisms of the corresponding AF algebra’s dimension group are then studied by utilizing this graph. This will also provide information about the automorphism groups of the corresponding AF algebras.
منابع مشابه
The Classification of Two-component Cuntz-krieger Algebras
Cuntz-Krieger algebras with exactly one non-trivial closed ideal are classiied up to stable isomorphism by the Cuntz invariant. The proof relies on RRrdam's classiication of simple Cuntz-Krieger algebras up to stable isomorphism and the author's classiication of two-component reducible topological Markov chains up to ow equivalence.
متن کاملAf -algebras and Topology of 3-manifolds
We consider 3-dimensional manifolds, which are surface bundles over the circle. It is shown that to every infinite order (pseudo-Anosov) monodromy φ of the bundle, one can assign an AF -algebra Aφ (an operator algebra). It is proved that the assignment is functorial, i.e. each monodromy φ, conjugate to φ, maps to an AF -algebra Aφ′ , which is stably isomorphic to Aφ. This approach gives new top...
متن کامل1 1 M ar 2 00 9 AF - algebras and topology of 3 - manifolds
We consider 3-dimensional manifolds, which are surface bundles over the circle. It is shown that to every infinite order (pseudo-Anosov) monodromy φ of the bundle, one can assign an AF -algebra Aφ (an operator algebra). It is proved that the assignment is functorial, i.e. each monodromy φ, conjugate to φ, maps to an AF -algebra Aφ′ , which is stably isomorphic to Aφ. This approach gives new top...
متن کاملStrong Topological Regularity and Weak Regularity of Banach Algebras
In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...
متن کاملVarious topological forms of Von Neumann regularity in Banach algebras
We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2005 شماره
صفحات -
تاریخ انتشار 2005