2024/05/23 by Anindya Ghatak, Narayan Rakshit, Ghatak, Anindya +5
Computer Science · Engineering · Mathematics · #20E08 #30H10 #32A35 #46L05 #47A13 #47A20 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Modular Robots and Swarm Intelligence #Operator Algebras (math.OA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2405.14157
openalex publication_date 2024/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a natural number n ≥ 1, the odometer semigroup On, also known as the adding machine or the Baumslag-Solitar monoid with two generators, is a well-known object in group theory. This paper examines the odometer semigroup in relation to representations of bounded linear operators. We focus on noncommutative operators and prove that contractive representations of On always admit to nicer representations of On. We give a complete description of representations of On on the Fock space and relate it to the odometer lifting and subrepresentations of On. Along the way, we also classify Nica covariant representations of On.