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

Symmetry Integrability and Geometry-Methods and Applications

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