Abstract
We propose a boundary quotient diagram for right LCM semigroups with property (AR) that generalizes the boundary quotient diagram for \(\mathbb {N}\rtimes \mathbb {N}^\times \). Our approach focuses on two important subsemigroups: the core subsemigroup and the semigroup of core irreducible elements. The diagram is then employed to unify several case studies on KMS-states, and we end with a discussion on K-theoretical aspects of the diagram motivated by recent findings for integral dynamics.
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Acknowledgements
The author would like to thank Nadia S. Larsen, Nathan Brownlowe, Selçuk Barlak, Dave Robertson, and Magnus Dahler Norling for stimulating discussions. Parts of this research were carried out during a visit to the University of Wollongong, and the author would like to express his gratitude for the great hospitality of its operator algebra group. The author thanks the referee for suggestions leading to an improved exposition in Sect. 5.
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Communicated by Benjamin Steinberg.
The author was supported by ERC through AdG 267079 and by RCN through FRIPRO 240362.
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Stammeier, N. A boundary quotient diagram for right LCM semigroups. Semigroup Forum 95, 539–554 (2017). https://doi.org/10.1007/s00233-017-9850-0
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DOI: https://doi.org/10.1007/s00233-017-9850-0