Inverse semigroups and the Cuntz-Li algebras

2011/04/06 by S. Sundar, Sundar, S. · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Mechanics and Applications

paper · pdf · doi:10.48550/arxiv.1104.1085

openalex publication_date 2011/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we apply the theory of inverse semigroups to the C^*-algebra U[ℤ] considered in \citeCuntz. We show that the C^*-algebra U[ℤ] is generated by an inverse semigroup of partial isometries. We explicity identify the groupoid G_tight associated to the inverse semigroup and show that G_tight is exactly the same groupoid obtained in \citeCuntz-Li.

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• Cuntz-Li relations, Inverse semigroups and Groupoids

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