We study invariants for shifts of finite type obtained as the K-theory ofvarious C*-algebras associated with them. These invariants have been studiedintensely over the past thirty years since their introduction by WolfgangKrieger. They may be given quite concrete descriptions as inductive limits ofsimplicially ordered free abelian groups. Shifts of finite type are specialcases of Smale spaces and, in earlier work, the second author has shown thatthe hyperbolic structure of the dynamics in a Smale space induces natural ringand module structures on certain of these K-groups. Here, we restrict ourattention to the special case of shifts of finite type and obtain explicitdescriptions in terms of the inductive limits.
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