Back to Search
Start Over
A geometric model for semilinear locally gentle algebras
- Publication Year :
- 2024
-
Abstract
- 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.<br />Comment: 36 pages, comments welcome
- Subjects :
- Mathematics - Representation Theory
Primary 16G20, Secondary 05E10, 05C10, 16D90
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2402.04947
- Document Type :
- Working Paper