On the KK-theory of strongly self-absorbing C*-algebras
| dc.creator | Dadarlat, Marius | |
| dc.creator | Winter, Wilhelm | |
| dc.date | 2007-04-04 | |
| dc.date.accessioned | 2026-07-07T07:54:33Z | |
| dc.date.available | 2026-07-07T07:54:33Z | |
| dc.description | Let $\Dh$ and $A$ be unital and separable $C^{*}$-algebras; let $\Dh$ be strongly self-absorbing. It is known that any two unital $^*$-homomorphisms from $\Dh$ to $A \otimes \Dh$ are approximately unitarily equivalent. We show that, if $\Dh$ is also $K_{1}$-injective, they are even asymptotically unitarily equivalent. This in particular implies that any unital endomorphism of $\Dh$ is asymptotically inner. Moreover, the space of automorphisms of $\Dh$ is compactly-contractible (in the point-norm topology) in the sense that for any compact Hausdorff space $X$, the set of homotopy classes $[X,\Aut(\Dh)]$ reduces to a point. The respective statement holds for the space of unital endomorphisms of $\Dh$. As an application, we give a description of the Kasparov group $KK(\Dh, A\ot \Dh)$ in terms of $^*$-homomorphisms and asymptotic unitary equivalence. Along the way, we show that the Kasparov group $KK(\Dh, A\ot \Dh)$ is isomorphic to $K_0(A\ot \Dh)$. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/0704.0583 | |
| dc.identifier | http://arxiv.org/abs/0704.0583 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126651 | |
| dc.subject | Operator Algebras | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 46L05; 47L40 | |
| dc.title | On the KK-theory of strongly self-absorbing C*-algebras | |
| dc.type | text |