To save unnecessary repetition, throughout this work, unless the contrary is explicitly stated, all inverse semigroups are countable, all locally compact Hausdorff spaces have a countable basis, all Hilbert spaces are separable and all representations of *-algebras on Hilbert spaces are assumed non-degenerate.1
KeywordsInverse Semigroup Partial Isometry Compact Hausdorff Space Inverse Subsemigroup Cuntz Algebra
Unable to display preview. Download preview PDF.
- 1.So for us, a representation of a *-algebra A on a Hilbert space H is a *-homomorphism T from A into B(H) such that the span of the vectors T(a)(ξ), where a ∈ A and ξ ∈ H, is dense in H.Google Scholar
- 2.In the book, bold face (as in 4.5) will be used for section references to distinguish them from equation references.Google Scholar
- 3.An account of noncommutative geometry with particular relevance to physical theories is given in the book by Landi ().Google Scholar
- 4.Often the symbol s is used for the source map. However, like Renault (), we have preferred to use d for this map, reserving s for an inverse semigroup element.Google Scholar
- 5.A discussion of Ehresmann’s work on ordered groupoids is given by Mark Lawson in his book .Google Scholar