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Ordered ∗-Semigroups and a C∗-Correspondence for a Partial Isometry
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Ordered ∗-Semigroups and a C∗-Correspondence for a Partial Isometry
Інший ID:
2010 Mathematics Subject Classification: 46L05; 46L08; 20M30; 06F05; 46L55
DOI:10.3842/SIGMA.2014.055
DOI:10.3842/SIGMA.2014.055
Посилання:
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.
Підтримка:
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.
Дата:
2014
Переглядів:
487
Завантажень:
240
Анотація:
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.
