• Alan L. T. Paterson
Part of the Progress in Mathematics book series (PM, volume 170)


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


Inverse Semigroup Partial Isometry Compact Hausdorff Space Inverse Subsemigroup Cuntz Algebra 
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  1. 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. 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. 3.
    An account of noncommutative geometry with particular relevance to physical theories is given in the book by Landi ([151]).Google Scholar
  4. 4.
    Often the symbol s is used for the source map. However, like Renault ([230]), we have preferred to use d for this map, reserving s for an inverse semigroup element.Google Scholar
  5. 5.
    A discussion of Ehresmann’s work on ordered groupoids is given by Mark Lawson in his book [157].Google Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Alan L. T. Paterson
    • 1
  1. 1.Department of MathematicsUniversity of MississippiUniversityUSA

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