Symmetries of Kirchberg algebras
| dc.creator | Benson, David J. | |
| dc.creator | Kumjian, Alex | |
| dc.creator | Phillips, N. Christopher | |
| dc.date | 2003-02-22 | |
| dc.date.accessioned | 2026-07-07T04:55:29Z | |
| dc.date.available | 2026-07-07T04:55:29Z | |
| dc.description | Let A be a separable unital nuclear purely infinite simple C*-algebra satisfying the Universal Coefficient Theorem, and such that the K_0-class of the identity is zero. We prove that every automorphism of order two of the K-theory of A is implemented by an automorphism of A of order two. As a consequence, we prove that every countable Z/2Z-graded module over the representation ring of Z/2Z is isomorphic to the equivariant K-theory for some action of Z/2Z on a separable unital nuclear purely infinite simple C*-algebra. Along the way, we prove that every not necessarily finitely generated module over the group ring of Z/2Z which is free as an abelian group has a direct sum decomposition with only three kinds of summands, namely the group ring itself and Z on which the nontrivial element of Z/2Z acts either trivially or by multiplication by -1. | |
| dc.description | 18 pages, AMSLaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0302273 | |
| dc.identifier | http://arxiv.org/abs/math/0302273 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66598 | |
| dc.subject | Operator Algebras | |
| dc.subject | 20C10, 46L55 (Primary) 19K99, 19L47, 46L40, 46L80 (Secondary) | |
| dc.title | Symmetries of Kirchberg algebras | |
| dc.type | text |