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GRAPH PRODUCTS AND THE ABSENCE OF PROPERTY (AR)

Part of: Selfadjoint operator algebras Semigroups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  16 October 2017

NICOLAI STAMMEIER
NICOLAI STAMMEIER*
Affiliation:
Department of Mathematics, University of Oslo, PO Box 1053 Blindern, NO-0316 Oslo, Norway email nicolsta@math.uio.no
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Abstract

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We discuss the internal structure of graph products of right LCM semigroups and prove that there is an abundance of examples without property (AR). Thereby we provide the first examples of right LCM semigroups lacking this seemingly common feature. The results are particularly sharp for right-angled Artin monoids.

Keywords

right LCM monoidsright-angled Artin monoidssemigroup C∗ -algebrasKMS-statesgeneralised scales

MSC classification

Primary: 20M10: General structure theory
Secondary: 20F36: Braid groups; Artin groups 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 104 , Issue 2 , April 2018 , pp. 274 - 288
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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