Ordered ∗-Semigroups and a C∗-Correspondence for a Partial Isometry
Certain ∗-semigroups are associated with the universal C∗-algebra generated by a partial isometry, which is itself the universal C∗-algebra of a ∗-semigroup. A fundamental role for a ∗-structure on a semigroup is emphasized, and ordered and matricially ordered ∗-semigroups are introduced, along with...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2014 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2014
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146684 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Ordered ∗-Semigroups and a C∗-Correspondence for a Partial Isometry / B. Brenken // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 20 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862734089982836736 |
|---|---|
| author | Brenken, B. |
| author_facet | Brenken, B. |
| citation_txt | Ordered ∗-Semigroups and a C∗-Correspondence for a Partial Isometry / B. Brenken // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Certain ∗-semigroups are associated with the universal C∗-algebra generated by a partial isometry, which is itself the universal C∗-algebra of a ∗-semigroup. A fundamental role for a ∗-structure on a semigroup is emphasized, and ordered and matricially ordered ∗-semigroups are introduced, along with their universal C∗-algebras. The universal C∗-algebra generated by a partial isometry is isomorphic to a relative Cuntz-Pimsner C∗-algebra of a C∗-correspondence over the C∗-algebra of a matricially ordered ∗-semigroup. One may view the C∗-algebra of a partial isometry as the crossed product algebra associated with a dynamical system defined by a complete order map modelled by a partial isometry acting on a matricially ordered ∗-semigroup.
|
| first_indexed | 2025-12-07T19:40:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146684 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:40:39Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Brenken, B. 2019-02-10T18:11:16Z 2019-02-10T18:11:16Z 2014 Ordered ∗-Semigroups and a C∗-Correspondence for a Partial Isometry / B. Brenken // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 46L05; 46L08; 20M30; 06F05; 46L55 DOI:10.3842/SIGMA.2014.055 https://nasplib.isofts.kiev.ua/handle/123456789/146684 Certain ∗-semigroups are associated with the universal C∗-algebra generated by a partial isometry, which is itself the universal C∗-algebra of a ∗-semigroup. A fundamental role for a ∗-structure on a semigroup is emphasized, and ordered and matricially ordered ∗-semigroups are introduced, along with their universal C∗-algebras. The universal C∗-algebra generated by a partial isometry is isomorphic to a relative Cuntz-Pimsner C∗-algebra of a C∗-correspondence over the C∗-algebra of a matricially ordered ∗-semigroup. One may view the C∗-algebra of a partial isometry as the crossed product algebra associated with a dynamical system defined by a complete order map modelled by a partial isometry acting on a matricially ordered ∗-semigroup. This paper is a contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in
 honor of Marc A. Rief fel. The full collection is available at http://www.emis.de/journals/SIGMA/Rieffel.html. 
 I am most grateful to the referees for their detailed and helpful commentary regarding the many
 changes aimed at improving the readability of my initial submission. As well, a referee suggested
 a shorter proof of Proposition 3.5 and pointed out the potential for a natural approach to the
 pair of ∗-maps ω and βω of Section 3.1. I am also thankful to the Fields Institute for their
 hospitality throughout the fall of 2012 during which some of this project was completed. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Ordered ∗-Semigroups and a C∗-Correspondence for a Partial Isometry Article published earlier |
| spellingShingle | Ordered ∗-Semigroups and a C∗-Correspondence for a Partial Isometry Brenken, B. |
| title | Ordered ∗-Semigroups and a C∗-Correspondence for a Partial Isometry |
| title_full | Ordered ∗-Semigroups and a C∗-Correspondence for a Partial Isometry |
| title_fullStr | Ordered ∗-Semigroups and a C∗-Correspondence for a Partial Isometry |
| title_full_unstemmed | Ordered ∗-Semigroups and a C∗-Correspondence for a Partial Isometry |
| title_short | Ordered ∗-Semigroups and a C∗-Correspondence for a Partial Isometry |
| title_sort | ordered ∗-semigroups and a c∗-correspondence for a partial isometry |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146684 |
| work_keys_str_mv | AT brenkenb orderedsemigroupsandaccorrespondenceforapartialisometry |