A geometric model for semilinear locally gentle algebras
We consider certain generalizations of gentle algebras that we call semilinear locally gentle algebras. These rings are examples of semilinear clannish algebras as introduced by the second author and Crawley-Boevey. We generalise the notion of a nodal algebra from work of Burban and Drozd and prove...
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Main Authors | , , , |
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Format | Journal Article |
Language | English |
Published |
07.02.2024
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Subjects | |
Online Access | Get full text |
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Summary: | We consider certain generalizations of gentle algebras that we call
semilinear locally gentle algebras. These rings are examples of semilinear
clannish algebras as introduced by the second author and Crawley-Boevey. We
generalise the notion of a nodal algebra from work of Burban and Drozd and
prove that semilinear gentle algebras are nodal by adapting a theorem of
Zembyk. We also provide a geometric realization of Zembyk's proof, which
involves cutting the surface into simpler pieces in order to endow our locally
gentle algebra with a semilinear structure. We then consider this surface glued
back together, with the seams in place, and use it to give a geometric model
for the finite-dimensional modules over the semilinear locally gentle algebra. |
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DOI: | 10.48550/arxiv.2402.04947 |