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Generalizations of free monoids

Published 27 Mar 2024 in math.CT | (2403.18449v2)

Abstract: We generalize free monoids by defining $k$-monoids. These are nothing other than the one-vertex higher-rank graphs used in $C{\ast}$-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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