- Title
- Product systems of graphs and the Toeplitz algebras of higher-rank graphs
- Creator
- Raeburn, Iain; Sims, Aidan
- Relation
- Journal of Operator Theory Vol. 53, no. 2, p. 399-429
- Publisher
- National Institute for Scientific and Technical Creation, Dept. of Mathematics
- Resource Type
- journal article
- Date
- 2005
- Description
- There has recently been much interest in the C*-algebras of directed graphs. Here we consider product systems E of directed graphs over sernigroups and associated C*-algebras C* (E) and TC* (E) which generalise the higher-rank graph algebras of Kumjian-Pask and their Toeplitz analogues. We study these algebras by constructing from E a product system X(E) of Hilbert bimodules, and applying recent results of Fowler about the Toeplitz algebras of such systems. Fowler's hypotheses turn out to be very interesting graph-theoretically, and indicate new relations which will have to be added to the usual Cuntz-Krieger relations to obtain a satisfactory theory of Cuntz-Krieger algebras for product systems of graphs; our algebras C* (E) and TC* (E) are universal for families of partial isometries satisfying these relations. Our main result is a uniqueness theorem for TC*(E) which has particularly interesting implications for the C*-algebras of non-row-finite higher-rank graphs. This theorem is apparently beyond the reach of Fowler's theory, and our proof requires a detailed analysis of the expectation onto the diagonal in TC*(E).
- Subject
- C*-algebra of directed graphs; Hilbert bimodules; Toeplitz algebras; product systems of graphs; c-asterisk-algebras; cuntz-krieger algebras; hilbert bimodules; infinite-graphs; cstar-algebras
- Identifier
- http://hdl.handle.net/1959.13/25304
- Identifier
- uon:424
- Identifier
- ISSN:0379-4024
- Language
- eng
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