Ordered ∗-Semigroups and a C∗-Correspondence for a Partial Isometry

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2014
• Main Author: Brenken, B.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2014
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146684
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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.