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Brauer configuration algebras: A generalization of Brauer graph algebras

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journal contribution
posted on 27.07.2017, 15:42 by Edward L. Green, Sibylle Schroll
In this paper we introduce a generalization of a Brauer graph algebra which we call a Brauer configuration algebra. As with Brauer graphs and Brauer graph algebras, to each Brauer configuration, there is an associated Brauer configuration algebra. We show that Brauer configuration algebras are finite dimensional symmetric algebras. After studying and analysing structural properties of Brauer configurations and Brauer configuration algebras, we show that a Brauer configuration algebra is multiserial; that is, its Jacobson radical is a sum of uniserial modules whose pairwise intersection is either zero or a simple module. The paper ends with a detailed study of the relationship between radical cubed zero Brauer configuration algebras, symmetric matrices with non-negative integer entries, finite graphs and associated symmetric radical cubed zero algebras.

Funding

This work was supported through the Engineering and Physical Sciences Research Council, grant number EP/K026364/1, UK and by the University of Leicester in form of a study leave for the second author

History

Citation

Bulletin des Sciences Mathématiques, 2017, 141 (6), pp. 539-572

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

AM (Accepted Manuscript)

Published in

Bulletin des Sciences Mathématiques

Publisher

Elsevier

issn

0007-4497

Acceptance date

28/04/2017

Copyright date

2017

Available date

06/06/2018

Publisher version

http://www.sciencedirect.com/science/article/pii/S0007449717300532

Notes

The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.;MSC 16G20; 16D50

Language

en