The profinite Schützenberger group defined by a symbolic dynamical system

Abstract: In finite semigroup theory, free profinite semigroups play a very important role. Around 2005, Almeida introduced a connection with symbolic dynamics that proved to be helpful to understand their structure. One of the most relevant aspects of this connection is the association between an irreducible symbolic dynamical system X and the Schützenberger group G(X) of a special regular J-class, defined by X, of the free profinite semigroup over the alphabet of X.

The profinite group G(X) is a dynamical invariant. In the case of minimal systems, it has a sort of geometric interpretation: it is the inverse limit of the profinite completions of the fundamental groups of the finite Rauzy graphs of X.

In this talk, after introducing the basic concepts involved, we survey some of the main results about the group G(X), ending, if time permits, with an application to the theory of codes.

category theorygroup theoryrings and algebras

Audience: researchers in the topic

York semigroup seminar

Series comments: Description: Semigroup-related research talks at University of York.

Email Nora Szakacs at nora.szakacs@york.ac.uk for the meeting password.