Product systems over right-angled Artin semigroups

Authors

Neal J. Fowler, University of Newcastle
Aidan Sims, University of WollongongFollow

RIS ID

16505

Publication Details

Fowler, N. J. & Sims, A. (2002). Product systems over right-angled Artin semigroups. Transactions of the American Mathematical Society, 354 (4), 1487-1509.

Abstract

We build upon MacLane's definition of a tensor category to introduce the concept of a product system that takes values in a tensor groupoid G. We show that the existing notions of product systems fit into our categorical framework, as do the k-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 G. In particular, we obtain necessary and sufficient conditions under which a collection of k 1-graphs form the coordinate graphs of a k-graph.