Contractive representations of odometer semigroup
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918037397962752 |
|---|---|
| author | Ghatak, Anindya Rakshit, Narayan Sarkar, Jaydeb Suryawanshi, Mansi |
| author_facet | Ghatak, Anindya Rakshit, Narayan Sarkar, Jaydeb Suryawanshi, Mansi |
| contents | 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 $O_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14157 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Contractive representations of odometer semigroup Ghatak, Anindya Rakshit, Narayan Sarkar, Jaydeb Suryawanshi, Mansi Functional Analysis Complex Variables Group Theory Operator Algebras 47A13, 46L05, 47A20, 30H10, 20E08, 32A35 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 $O_n$. |
| title | Contractive representations of odometer semigroup |
| topic | Functional Analysis Complex Variables Group Theory Operator Algebras 47A13, 46L05, 47A20, 30H10, 20E08, 32A35 |
| url | https://arxiv.org/abs/2405.14157 |