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KMS states on $C_c^{*}(\mathbb{N}^2)$

Part of: Selfadjoint operator algebras Semigroups

Published online by Cambridge University Press:  03 April 2023

Anbu Arjunan ,
Sruthymurali  and
S. Sundar
Anbu Arjunan
Affiliation:
Indian Statistical Institute, Delhi Centre, NewDelhi, 110016, India
Sruthymurali
Affiliation:
Indian Statistical Institute, Bangalore Centre, Bangalore, 560059, India
S. Sundar*
Affiliation:
Institute of Mathematical Sciences (HBNI), Chennai, 600113, India
*
*Corresponding author. E-mail: [email protected]
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Abstract

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.

Keywords

KMS statesSemigroupsGroupoids

MSC classification

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 46L30: States 20M99: None of the above, but in this section
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 65 , Issue 3 , September 2023 , pp. 501 - 528
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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