Generalizations of free monoids

Mark V. Lawson; Alina Vdovina

doi:10.1007/s00233-024-10450-w

Generalizations of free monoids

Mark V. Lawson^*, Alina Vdovina

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	167-185
Number of pages	19
Journal	Semigroup Forum
Volume	109
Issue number	1
Early online date	12 Jul 2024
DOIs	https://doi.org/10.1007/s00233-024-10450-w
Publication status	Published - Aug 2024

Keywords

Free monoids
Higher rank graphs
The Thompson–Higman groups

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/s00233-024-10450-w

Cite this

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abstract = "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.",

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AB - 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.

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KW - The Thompson–Higman groups

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Generalizations of free monoids

Abstract

Keywords

ASJC Scopus subject areas

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