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- W2120990055 abstract "We prove that there is a correspondence between self-similar group actions and the class of left cancellative right hereditary monoids satisfying the dedekind height property. The monoids in question turn out to be coextensive with the Zappa-Sz ep products of free monoids and groups, and the ideal structure of the monoid reects properties of the group action. These monoids can also be viewed as ‘tensor monoids’ of covering bimodules, and also arise naturally from a double category associated with the action. There is also a correspondence between self-similar group actions and a class of inverse monoids, which are congruence-free when the actions are faithful; these inverse monoids arise naturally in the construction of the Cuntz-Pimsner algebras associated with the actions, and generalise the polycyclic monoids from which the Cuntz algebras are constructed. Finally, these results have the eect of correcting an error in a paper of Nivat and Perrot." @default.
- W2120990055 created "2016-06-24" @default.
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- W2120990055 date "2006-01-01" @default.
- W2120990055 modified "2023-09-27" @default.
- W2120990055 title "A monoid associated with a self-similar group action" @default.
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