2024/02/07 by Esther Banaian, Banaian, Esther, Raphael Bennett‐Tennenhaus +5
Computer Science · Mathematics · #05C10 #16D90 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Primary 16G20 #Representation Theory (math.RT) #Secondary 05E10
paper · pdf · doi:10.48550/arxiv.2402.04947
openalex publication_date 2024/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.