Smale space 𝐶*-algebras have nonzero projections

Deeley, Robin; Goffeng, Magnus; Yashinski, Allan

doi:10.1090/proc/14837

Smale space $C^*$-algebras have nonzero projections
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by Robin J. Deeley, Magnus Goffeng and Allan Yashinski PDF

Proc. Amer. Math. Soc. 148 (2020), 1625-1639 Request permission

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.

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