Generalizations of free monoids

Generalizations of free monoids

We generalize free monoids by defining k -monoids. These are nothing other than the one-vertex higher-rank graphs used in C ∗ -algebra theory with the cardinality requirement waived. The 1-monoids are precisely the free monoids. We then take the next step and generalize k -monoids in such a way that...

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Veröffentlicht in:Semigroup forum 2024-08, Vol.109 (1), p.167-185
Hauptverfasser: Lawson, Mark V., Vdovina, Alina
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Mathematics
Mathematics and Statistics
Monoids
Research Article
Self-similarity
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Zusammenfassung:We generalize free monoids by defining k -monoids. These are nothing other than the one-vertex higher-rank graphs used in C ∗ -algebra theory with the cardinality requirement waived. The 1-monoids are precisely the free monoids. We then take the next step and generalize k -monoids in such a way that self-similar group actions yield monoids of this type.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-024-10450-w