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Smale space C*-algebras have non-zero projections

Goffeng, Carl Henrik Tryggve Magnus LU ; Deeley, Robin and Yashinski, Allan (2020) In Proceedings of the American Mathematical Society 148(4). p.1625-1639
Abstract
The main result of the present paper is that the stable and unstable $C^*$-algebras associated to a mixing Smale space always contain nonzero projections. This gives a positive answer to a question of the first listed author and Karen Strung and has implications for the structure of these algebras in light of the Elliott program for simple $C^*$-algebras. Using our main result, we also show that the homoclinic, stable, and unstable algebras each have real rank zero.
Please use this url to cite or link to this publication:
author
; and
publishing date
type
Contribution to journal
publication status
published
subject
in
Proceedings of the American Mathematical Society
volume
148
issue
4
pages
1625 - 1639
publisher
American Mathematical Society (AMS)
external identifiers
  • scopus:85080863492
ISSN
1088-6826
DOI
10.1090/proc/14837
language
English
LU publication?
no
id
6634e805-450e-4abc-880c-79f7cfeaa030
date added to LUP
2021-03-12 12:02:09
date last changed
2022-04-19 05:06:59
@article{6634e805-450e-4abc-880c-79f7cfeaa030,
  abstract     = {{The main result of the present paper is that the stable and unstable $C^*$-algebras associated to a mixing Smale space always contain nonzero projections. This gives a positive answer to a question of the first listed author and Karen Strung and has implications for the structure of these algebras in light of the Elliott program for simple $C^*$-algebras. Using our main result, we also show that the homoclinic, stable, and unstable algebras each have real rank zero.}},
  author       = {{Goffeng, Carl Henrik Tryggve Magnus and Deeley, Robin and Yashinski, Allan}},
  issn         = {{1088-6826}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{1625--1639}},
  publisher    = {{American Mathematical Society (AMS)}},
  series       = {{Proceedings of the American Mathematical Society}},
  title        = {{Smale space C*-algebras have non-zero projections}},
  url          = {{http://dx.doi.org/10.1090/proc/14837}},
  doi          = {{10.1090/proc/14837}},
  volume       = {{148}},
  year         = {{2020}},
}