2025/04/13 by Caranguay-Mainguez, Jhony F., Rizzo, Pedro, Vélez-Marulanda, José A.
#16G10 (Primary) 16G20 #16G70 (Secondary) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2504.09678
Let \Bbbk be an algebraically closed field and Λ a generalized Brauer tree algebra over \Bbbk. We compute the universal deformation rings of the periodic string modules over Λ. Moreover, for a specific class of generalized Brauer tree algebras Λ(n,m), we classify the universal deformation rings of the modules lying in Ω-stable components \mathfrakC of the stable Auslander-Reiten quiver provided that \mathfrakC contains at least one simple module. Our approach uses several tools and techniques from the representation theory of Brauer graph algebras. Notably, we leverage Duffield's work on the Auslander-Reiten theory of these algebras and Opper-Zvonareva's results on derived equivalences between Brauer graph algebras.