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CONNECTIVITY PROPERTIES OF MCKAY QUIVERS

Part of: Representation theory of groups Graph theory

Published online by Cambridge University Press:  02 October 2020

HAZEL BROWNE Open the ORCID record for HAZEL BROWNE [Opens in a new window]
HAZEL BROWNE*
Affiliation:
School of Mathematics and Statistics, The University of Sydney, Camperdown, New South Wales 2006, Australia
*
e-mail: hbro4811@uni.sydney.edu.au
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Abstract

We present several results on the connectivity of McKay quivers of finite-dimensional complex representations of finite groups, with no restriction on the faithfulness or self-duality of the representations. We give examples of McKay quivers, as well as quivers that cannot arise as McKay quivers, and discuss a necessary and sufficient condition for two finite groups to share a connected McKay quiver.

Keywords

McKay quiverscomplex representations of finite groupsconnectivity of quivers

MSC classification

Primary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Secondary: 20C05: Group rings of finite groups and their modules 20C15: Ordinary representations and characters
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 2 , April 2021 , pp. 182 - 194
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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