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GROUP ACTIONS AND COVERINGS OF BRAUER GRAPH ALGEBRAS

Published online by Cambridge University Press:  30 August 2013

EDWARD L. GREEN ,
SIBYLLE SCHROLL  and
NICOLE SNASHALL
EDWARD L. GREEN
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, USA e-mail: [email protected]
SIBYLLE SCHROLL
Affiliation:
Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom e-mail: [email protected]
NICOLE SNASHALL
Affiliation:
Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom e-mail: [email protected]
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Abstract

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We develop a theory of group actions and coverings on Brauer graphs that parallels the theory of group actions and coverings of algebras. In particular, we show that any Brauer graph can be covered by a tower of coverings of Brauer graphs such that the topmost covering has multiplicity function identically one, no loops, and no multiple edges. Furthermore, we classify the coverings of Brauer graph algebras that are again Brauer graph algebras.

Keywords

Primary 05E1816G20Secondary 14E2016W5058E40
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 2 , May 2014 , pp. 439 - 464
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

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