For the case of shift spaces over finite alphabets, Kitchens (Ergodic Theory Dyn. Syst., vol. 7, 2) proved that any group shift is isomorphic to a full shift product a finite set.

In this work we extend the above result for shift spaces over countable alphabets. In the case, that the alphabet is infinite, we can use either the usual definition of shift spaces or the Ott-Tomforde-Willis compactification scheme. In any case, we can prove that inverse semigroup shifts are always isomorphic to a full shift (over a countable alphabet) product a special type of shift spaces which we named ‘fractal shifts’.

This is a joint work with D. Gonçalves (UFSC-Brazil) and C. Starling (uOttawa-Canada). This work was supported by CNPq-Brazil and Capes-Brazil grants.