Geometric realization and K-theoretic decomposition of C*-algebras
| dc.creator | Schochet, Claude | |
| dc.date | 2001-07-06 | |
| dc.date.accessioned | 2026-07-07T04:42:30Z | |
| dc.date.available | 2026-07-07T04:42:30Z | |
| dc.description | Suppose that A is a separable C*-algebra and that G_* is a (graded) subgroup of K_*(A). Then there is a natural short exact sequence 0 \to G_* \to K_*(A) \to K_*(A)/G_* \to 0. In this note we demonstrate how to geometrically realize this sequence at the level of C*-algebras. As a result, we KK-theoretically decompose A as 0 \to A\otimes \Cal K \to A_f \to SA_t \to 0 where K_*(A_t) is the torsion subgroup of K_*(A) and K_*(A_f) is its torsionfree quotient. Then we further decompose A_t : it is KK-equivalent to \oplus_p A_p where K_*(A_p) is the p-primary subgroup of the torsion subgroup of K_*(A). We then apply this realization to study the Kasparov group K^*(A) and related objects. | |
| dc.description | 9 pages.To appear in International J. Math | |
| dc.identifier | https://arxiv.org/abs/math/0107042 | |
| dc.identifier | http://arxiv.org/abs/math/0107042 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61808 | |
| dc.subject | Operator Algebras | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 46L80, 19K35, 46L85 | |
| dc.title | Geometric realization and K-theoretic decomposition of C*-algebras | |
| dc.type | text |