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Journal Article

THE ANALYTIC ALGEBRAS OF HIGHER RANK GRAPHS

David W. Kribs and Stephen C. Power
Mathematical Proceedings of the Royal Irish Academy
Vol. 106A, No. 2 (December 2006), pp. 199-218
Published by: Royal Irish Academy
Stable URL: http://www.jstor.org/stable/40656946
Page Count: 20
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
THE ANALYTIC ALGEBRAS OF HIGHER RANK GRAPHS
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Abstract

We begin the study of a new class of operator algebras that arise from higher rank graphs. Every higher rank graph generates a Fock space Hubert space and creation operators that are partial isometries acting on the space. We call the weak operator topology closed algebra generated by these operators a ' higher rank semigroupoid algebra'. A number of examples are discussed in detail, including the single vertex case and higher rank cycle graphs. In particular, the cycle graph algebras are identified as matricial multivariable function algebras. We obtain reflexivity for a wide class of graphs and characterize semisimplicity in terms of the underlying graph.

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