Journal of Noncommutative Geometry

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Volume 11, Issue 2, 2017, pp. 537–579
DOI: 10.4171/JNCG/11-2-4

Published online: 2017-06-29

The Ext algebra of a Brauer graph algebra

Edward L. Green[1], Sibylle Schroll[2], Nicole Snashall[3] and Rachel Taillefer[4]

(1) Virginia Tech, Blacksburg, USA
(2) University of Leicester, UK
(3) University of Leicester, UK
(4) Université Clermont Auvergne, Université Blaise Pascal, Clermont-Ferrand, France

In this paper we study finite generation of the Ext algebra of a Brauer graph algebra by determining the degrees of the generators. As a consequence we characterize the Brauer graph algebras that are Koszul and those that are ${\mathcal K}_2$.

Keywords: Brauer graph algebra, Koszul, $d$-Koszul, Ext algebra, finite generation

Green Edward, Schroll Sibylle, Snashall Nicole, Taillefer Rachel: The Ext algebra of a Brauer graph algebra. J. Noncommut. Geom. 11 (2017), 537-579. doi: 10.4171/JNCG/11-2-4