Lifting KK-elements, asymptotical unitary equivalence and classification of simple C*-algebras
| dc.creator | Lin, Huaxin | |
| dc.creator | Niu, Zhuang | |
| dc.date | 2008-02-11 | |
| dc.date | 2008-03-10 | |
| dc.date.accessioned | 2026-07-07T09:25:30Z | |
| dc.date.available | 2026-07-07T09:25:30Z | |
| dc.description | Let $A$ and $C$ be two unital simple C*-algebas with tracial rank zero. Suppose that $C$ is amenable and satisfies the Universal Coefficient Theorem. Denote by ${KK}_e(C,A)^{++}$ the set of those $κ$ for which $κ(K_0(C)_+\setminus\{0\})\subset K_0(A)_+\setminus\{0\}$ and $κ([1_C])=[1_A]$. Suppose that $κ\in {KK}_e(C,A)^{++}.$ We show that there is a unital monomorphism $ϕ: C\to A$ such that $[ϕ]=κ.$ Suppose that $C$ is a unital AH-algebra and $λ: \mathrm{T}(A)\to \mathrm{T}_{\mathtt{f}}(C)$ is a continuous affine map for which $τ(κ([p]))=λ(τ)(p)$ for all projections $p$ in all matrix algebras of $C$ and any $τ\in \mathrm{T}(A),$ where $\mathrm{T}(A)$ is the simplex of tracial states of $A$ and $\mathrm{T}_{\mathtt{f}}(C)$ is the convex set of faithful tracial states of $C.$ We prove that there is a unital monomorphism $ϕ: C\to A$ such that $ϕ$ induces both $κ$ and $λ.$ Suppose that $h: C\to A$ is a unital monomorphism and $γ\in \mathrm{Hom}(\Kone(C), \aff(A)).$ We show that there exists a unital monomorphism $ϕ: C\to A$ such that $[ϕ]=[h]$ in ${KK}(C,A),$ $τ\circ ϕ=τ\circ h$ for all tracial states $τ$ and the associated rotation map can be given by $γ.$ Applications to classification of simple C*-algebras are also given. | |
| dc.description | The new version made a correction and removed a number of typos | |
| dc.identifier | https://arxiv.org/abs/0802.1484 | |
| dc.identifier | http://arxiv.org/abs/0802.1484 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156425 | |
| dc.subject | Operator Algebras | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 46L05, 46L80 | |
| dc.title | Lifting KK-elements, asymptotical unitary equivalence and classification of simple C*-algebras | |
| dc.type | text |