Contractive representations of odometer semigroup

Autor:	Ghatak, Anindya, Rakshit, Narayan, Sarkar, Jaydeb, Suryawanshi, Mansi
Rok vydání:	2024
Předmět:	Mathematics - Functional Analysis Mathematics - Complex Variables Mathematics - Group Theory Mathematics - Operator Algebras 47A13 46L05 47A20 30H10 20E08 32A35
Druh dokumentu:	Working Paper
Popis:	Given a natural number $n \geq 1$, the odometer semigroup $O_n$, 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 $O_n$ always admit to nicer representations of $O_n$. We give a complete description of representations of $O_n$ on the Fock space and relate it to the odometer lifting and subrepresentations of $O_n$. Along the way, we also classify Nica covariant representations of $O_n$. Comment: 29 pages. Revised
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.14157 Zobrazit plný text záznamu View this record from Arxiv