Symmetry Integrability and Geometry-Methods and Applications | |
Ordered *-Semigroups and a C * -Correspondence for a Partial Isometry | |
article | |
Berndt Brenken1  | |
[1] Department of Mathematics and Statistics, University of Calgary | |
关键词: C ∗ -algebras; partial isometry; ∗-semigroup; partial order; matricial order; completely positive maps; C ∗ -correspondence; Schwarz inequality; exact C ∗ -algebra; | |
DOI : 10.3842/SIGMA.2014.055 | |
来源: National Academy of Science of Ukraine | |
【 摘 要 】
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.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO202106300001343ZK.pdf | 691KB | download |