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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Product systems over right-angled Artin semigroups
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by Neal J. Fowler and Aidan Sims PDF
Trans. Amer. Math. Soc. 354 (2002), 1487-1509 Request permission

Abstract:

We build upon Mac Laneโ€™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 $k$-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 $\mathcal G$. In particular, we obtain necessary and sufficient conditions under which a collection of $k$ $1$-graphs form the coordinate graphs of a $k$-graph.
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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
  • MR Author ID: 671497
  • Received by editor(s): December 22, 1999
  • Received by editor(s) in revised form: June 28, 2001
  • Published electronically: November 30, 2001
  • © Copyright 2001 American Mathematical Society
  • 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
  • MathSciNet review: 1873016