 
Summary: Ergod. Th. & Dynam. Sys. (2003), 23, 14851504 c 2003 Cambridge University Press
DOI: 10.1017/S0143385702001700 Printed in the United Kingdom
Positive Ktheory for finitary isomorphisms
of Markov chains
RICARDO G ´OMEZ
Instituto de Matem´aticas, Area de la Investigaci´on Cient´ifica, Circuito Exterior,
Ciudad Universitaria, M´exico DF 04510, M´exico
(email: rgomez@math.unam.mx)
(Received 10 September 2001 and accepted in revised form 6 February 2003)
Abstract. We use matrices over formal power series to represent irreducible and positive
recurrent Markov chains and identify a natural class of good finitary isomorphisms
(magic word isomorphisms) as those arising from elementary matrix operations.
This extends the positive Ktheory framework which has been used for other classification
problems in symbolic dynamics.
1. Introduction
One of the significant recent developments in symbolic dynamics is the `positive Ktheory'
approach to classification and isomorphism [5], inaugurated in [13, 14] following earlier
applications of polynomial matrices [2, 3, 20, 31]. In the most important example, very
roughly, a shift of finite type is represented by a matrix A whose entries are polynomials
with Z+ coefficients; and multiplication of I  A by an elementary matrix satisfying a
