Asymptotically Unitary Equivalence and Classification of Simple Amenable C*-algebras
| dc.creator | Lin, Huaxin | |
| dc.date | 2008-06-03 | |
| dc.date | 2009-01-12 | |
| dc.date.accessioned | 2026-07-07T12:27:52Z | |
| dc.date.available | 2026-07-07T12:27:52Z | |
| dc.description | Let $C$ and $A$ be two unital separable amenable simple C*-algebras with tracial rank no more than one. Suppose that $C$ satisfies the Universal Coefficient Theorem and suppose that $ϕ_1, ϕ_2: C\to A$ are two unital monomorphisms. We show that there is a continuous path of unitaries $\{u_t: t\in [0, \infty)\}$ of $A$ such that $$ \lim_{t\to\infty}u_t^*ϕ_1(c)u_t=ϕ_2(c)\tforal c\in C $$ if and only if $[ϕ_1]=[ϕ_2]$ in $KK(C,A),$ $ϕ_1^‡=ϕ_2^‡,$ $(ϕ_1)_T=(ϕ_2)_T$ and a rotation related map $\bar{R}_{ϕ_1,ϕ_2}$ associated with $ϕ_1$ and $ϕ_2$ is zero. Applying this result together with a result of W. Winter, we give a classification theorem for a class ${\cal A}$ of unital separable simple amenable \CA s which is strictly larger than the class of separable \CA s whose tracial rank are zero or one. The class contains all unital simple ASH-algebras whose state spaces of $K_0$ are the same as the tracial state spaces as well as the simple inductive limits of dimension drop circle algebras. Moreover it contains some unital simple ASH-algebras whose $K_0$-groups are not Riesz. One consequence of the main result is that all unital simple AH-algebras which are ${\cal Z}$-stable are isomorphic to ones with no dimension growth. | |
| dc.identifier | https://arxiv.org/abs/0806.0636 | |
| dc.identifier | http://arxiv.org/abs/0806.0636 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215353 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L35, 46L80 | |
| dc.title | Asymptotically Unitary Equivalence and Classification of Simple Amenable C*-algebras | |
| dc.type | text |