Automorphisms of $\mathcal{B}$-free and other Toeplitz shifts

Abstract

We present sufficient conditions for the triviality of the automorphism group of regular Toeplitz subshifts and give a broad class of examples from the class of $\mathcal{B}$-free subshifts satisfying them, extending [10]. On the other hand we provide an example of a $\mathcal{B}$-free Toeplitz subshift whose automorphism group has elements of arbitrarily large finite order, answering Question 11 in [13].

39 pages, We worked out how much of the approach to the centralizer for B-free systems carries over to general Toeplitz shifts. We introduced essential holes at level n in the construction of a Toeplitz sequence which allows us to state our previous results for general Toeplitz shifts, see Section 2. In Section 3 we apply these results to B-free Toeplitz shifts