Product systems over right-angled Artin semigroups

Authors:
Neal J. Fowler and Aidan Sims

Journal:
Trans. Amer. Math. Soc. **354** (2002), 1487-1509

MSC (1991):
Primary 20F36; Secondary 18B40, 55N20

DOI:
https://doi.org/10.1090/S0002-9947-01-02911-7

Published electronically:
November 30, 2001

MathSciNet review:
1873016

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 . 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 . 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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Additional Information

**Neal J. Fowler**

Affiliation:
Department of Mathematics, University of Newcastle, NSW 2308, Australia

**Aidan Sims**

Affiliation:
Department of Mathematics, University of Newcastle, NSW 2308, Australia

DOI:
https://doi.org/10.1090/S0002-9947-01-02911-7

Received by editor(s):
December 22, 1999

Received by editor(s) in revised form:
June 28, 2001

Published electronically:
November 30, 2001

Article copyright:
© Copyright 2001
American Mathematical Society