Geodesic
KMS states on $C_c^{*}(\mathbb{N}^2)$
Glasgow mathematical journal, Tome 65 (2023) no. 3, pp. 501-528

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DOI

Let $C_c^{*}(\mathbb{N}^{2})$ be the universal $C^{*}$-algebra generated by a semigroup of isometries $\{v_{(m,n)}\,:\, m,n \in \mathbb{N}\}$ whose range projections commute. We analyse the structure of KMS states on $C_{c}^{*}(\mathbb{N}^2)$ for the time evolution determined by a homomorphism $c\,:\,\mathbb{Z}^{2} \to \mathbb{R}$. In contrast to the reduced version $C_{red}^{*}(\mathbb{N}^{2})$, we show that the set of KMS states on $C_{c}^{*}(\mathbb{N}^{2})$ has a rich structure. In particular, we exhibit uncountably many extremal KMS states of type I, II and III.
DOI : 10.1017/S0017089523000071
Mots-clés : KMS states, Semigroups, Groupoids 
Arjunan, Anbu; Sruthymurali; Sundar, S. KMS states on $C_c^{*}(\mathbb{N}^2)$. Glasgow mathematical journal, Tome 65 (2023) no. 3, pp. 501-528. doi: 10.1017/S0017089523000071
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     title = {KMS states on $C_c^{*}(\mathbb{N}^2)$},
     journal = {Glasgow mathematical journal},
     pages = {501--528},
     year = {2023},
     volume = {65},
     number = {3},
     doi = {10.1017/S0017089523000071},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089523000071/}
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