no. 3
Global dimensions of local geodesic ghor algebras
Baur, Karin1, 2 orcid; Beil, Charlie3 orcid 
1School of Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom
2Ruhr-Universität Bochum, Universitätsstrasse 150, D-44780 Bochum, Germany
3Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Heinrichstrasse 36, 8010 Graz, Austria
Annals of Representation Theory, Volume 3 (2026) no. 3, pp. 439-455

A ghor algebra is a path algebra with relations of a dimer quiver on a compact surface. We show that the global dimension of any cyclic localization of a geodesic ghor algebra on a genus $g \ge 1$ surface is bounded above by $2g+1$. This number coincides with the Krull dimension of the center of the ghor algebra. We further show that the bound is an equality if and only if the point of localization sits over the noetherian locus of the center.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/art.46
Classification: 16G20, 16S38, 16S50
Keywords: Dimer algebra, dimer model, Jacobian algebra, quiver with potential, global dimension.

Baur, Karin  1 , 2 ; Beil, Charlie  3

1 School of Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom
2 Ruhr-Universität Bochum, Universitätsstrasse 150, D-44780 Bochum, Germany
3 Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Heinrichstrasse 36, 8010 Graz, Austria
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Baur, Karin; Beil, Charlie. Global dimensions of local geodesic ghor algebras. Annals of Representation Theory, Volume 3 (2026) no. 3, pp. 439-455. doi: 10.5802/art.46
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