1. A generalization of cancellative dimer algebras to hyperbolic surfaces
- Author
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Baur, Karin and Beil, Charlie
- Subjects
Rings and Algebras (math.RA) ,FOS: Mathematics ,Mathematics - Rings and Algebras - Abstract
We study a new class of quiver algebras on surfaces, called 'geodesic ghor algebras'. These algebras generalize cancellative dimer algebras on a torus to higher genus surfaces, where the relations come from perfect matchings rather than a potential. Although cancellative dimer algebras on a torus are noncommutative crepant resolutions, the center of any dimer algebra on a higher genus surface is just the polynomial ring in one variable, and so the center and surface are unrelated. In contrast, we establish a rich interplay between the central geometry of geodesic ghor algebras and the topology of the surface in which they are embedded. Furthermore, we show that noetherian central localizations of such algebras are endomorphism rings of modules over their centers., 27 pages. The main results stated in the companion article arXiv:2101.10843 are proved here. Comments welcome!
- Published
- 2021