Transactions of the American Mathematical Society

Author(s): Neal J. Fowler; Aidan Sims
Journal: Trans. Amer. Math. Soc. 354 (2002), 1487-1509.
MSC (1991): Primary 20F36; Secondary 18B40, 55N20
Posted: November 30, 2001
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Abstract: We build upon Mac Lane's definition of a tensor category to introduce the concept of a product system that takes values in a tensor groupoid $\mathcal G$ . We show that the existing notions of product systems fit into our categorical framework, as do the

-graphs of Kumjian and Pask. We then specialize to product systems over right-angled Artin semigroups; these are semigroups that interpolate between free semigroups and free abelian semigroups. For such a semigroup we characterize all product systems which take values in a given tensor groupoid $\mathcal G$ . In particular, we obtain necessary and sufficient conditions under which a collection of

-graphs form the coordinate graphs of a

-graph.

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Neal J. Fowler
Affiliation: Department of Mathematics, University of Newcastle, NSW 2308, Australia

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ISSN 1088-6850(e) ISSN 0002-9947(p)

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