Larsen, N. S. and Li, X. (2012) The 2-adic ring C*-algebra of the integers and its representations. Journal of Functional Analysis, 262(4), pp. 1392-1426. (doi: 10.1016/j.jfa.2011.11.008)
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Abstract
We study the 2-adic version of the ring C* -algebra of the integers. First, we work out the precise relation between the Cuntz algebra O2 and our 2-adic ring C* -algebra in terms of representations. Secondly, we prove a 2-adic duality theorem identifying the crossed product arising from 2-adic affine transformations on the 2-adic numbers with the analogous crossed product algebra over the real numbers. And finally, as an outcome of this duality result, we construct an explicit imprimitivity bimodule and prove that it transports one canonical representation into the other.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Li, Professor Xin |
| Authors: | Larsen, N. S., and Li, X. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Journal of Functional Analysis |
| Publisher: | Elsevier |
| ISSN: | 0022-1236 |
| ISSN (Online): | 1096-0783 |
| Published Online: | 16 November 2011 |
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