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Functoriality of the C *‐Algebras Associated with Hyperbolic Dynamical Systems
Author(s) -
Putnam Ian F.
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s002461070000140x
Subject(s) - pure mathematics , mathematics , algebra over a field
The paper considers a mixing Smale space, the relations of stable and unstable equivalence on such a space and the C *‐algebras which are constructed from them. In general, these associations are not functorial. However, it is shown that, if one restricts to the class of s‐resolving, finite‐to‐one factor maps, then the construction of the stable C *‐algebra is contravariant, while that of the unstable C *‐algebra is covariant. The paper also discusses the constructions of these C *‐algebras for Smale spaces which are not mixing.