- Title
- The representation theory of numerical semigroups and the ideal structure of Exel's crossed product
- Creator
- Vittadello, Sean T.
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2008
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- We study representations of numerical semigroups Σ by isometries on Hilbert space with commuting range projections. Our main theorem says that each such representation is unitarily equivalent to the direct sum of a representation by unitaries and a finite number of multiples of particular concrete representations by isometries. We use our main theorem to identify the faithful representations of the C*-algebra C*(Σ) generated by a universal isometric representation with commuting range projections, and also prove a structure theorem for C*(Σ). We also investigate the ideal structure of Exel's crossed product C₀(T)⋊α,Lℕ. We give conditions describing precisely when C₀(T)⋊α,Lℕ is simple. We provide a complete description of the gauge-invariant ideals of C₀(T)⋊α,Lℕ, and give a condition which ensures that every ideal of C₀(T)⋊α,Lℕ is gauge invariant. Under the assumption that Τ is second countable, we describe the primitive ideal structure of C₀(T)⋊α,Lℕ.
- Subject
- C*-algebra; topological graph; graph algebra; ideal structure; Hilbert bimodule; numerical semigroup; crossed product; isometric representation; Wold decomposition; Toeplitz operator
- Identifier
- http://hdl.handle.net/1959.13/1418768
- Identifier
- uon:37393
- Rights
- Copyright 2008 Sean T. Vittadello
- Language
- eng
- Full Text
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| View Details Download | ATTACHMENT01 | Thesis | 768 KB | Adobe Acrobat PDF | View Details Download | ||
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