A geometric model for semilinear locally gentle algebras

Autor:	Banaian, Esther, Bennett-Tennenhaus, Raphael, Jacobsen, Karin M., Wright, Kayla
Rok vydání:	2024
Předmět:	Mathematics - Representation Theory Primary 16G20 Secondary 05E10 05C10 16D90
Druh dokumentu:	Working Paper
Popis:	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. Comment: 36 pages, comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2402.04947 Zobrazit plný text záznamu View this record from Arxiv