Inverse semigroup shifts over countable alphabets

In this work we characterize shift spaces over infinite countable alphabets that can be endowed with an inverse semigroup operation. We give sufficient conditions under which zero-dimensional inverse semigroups can be recoded as shift spaces whose correspondent inverse semigroup operation is a 1-blo...

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Bibliographic Details
Published in:Semigroup forum 2018-04, Vol.96 (2), p.203-240
Main Authors: Gonçalves, Daniel, Sobottka, Marcelo, Starling, Charles
Format: Article
Language:English
Subjects:
Algebra
Alphabets
Markov processes
Mathematics
Mathematics and Statistics
Research Article
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Summary:In this work we characterize shift spaces over infinite countable alphabets that can be endowed with an inverse semigroup operation. We give sufficient conditions under which zero-dimensional inverse semigroups can be recoded as shift spaces whose correspondent inverse semigroup operation is a 1-block operation, that is, it arises from a group operation on the alphabet. Motivated by this, we go on to study block operations on shift spaces and, in the end, we prove our main theorem, which states that Markovian shift spaces, which can be endowed with a 1-block inverse semigroup operation, are conjugate to the product of a full shift with a fractal shift.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-017-9858-5