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Brauer graph algebras

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posted on 07.02.2020 by Sibylle Schroll
These lecture notes on Brauer graph algebras are the result of a series of four lectures given at the CIMPA research school in Mar del Plata, Argentina, in March 2016. After motivating the study of Brauer graph algebras by relating them to special biserial algebras, the definition of Brauer graph algebras is given in great detail with many examples to illustrate the concepts. This is followed by a short section
on the interpretation of Brauer graphs as decorated ribbon graphs. A section on gentle algebras and their graphs, trivial extensions of gentle algebras, admissible cuts of Brauer graph algebras and a first connection of Brauer graph algebras with Jacobian algebras associated to triangulations of marked oriented surfaces follows. The interpretation
of flips of diagonals in triangulations of marked oriented surfaces as derived equivalences of Brauer graph algebras and the comparison of derived equivalences of Brauer graph algebras with derived equivalences of frozen Jacobian algebras is the topic of the next section. In the last section, after defining Green’s walk around the Brauer graph, a
complete description of the Auslander-Reiten quiver of a Brauer graph algebra is given.

History

Citation

arXiv:1612.00061

Author affiliation

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

Version

AO (Author's Original)

Published in

arXiv:1612.00061

Acceptance date

30/05/2017

Copyright date

2017

Available date

27/07/2017

Publisher version

https://arxiv.org/abs/1612.00061v3

Notes

55 pages, many figures and examples throughout, comments and suggestions welcome, minor corrections

Language

en

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