On universal deformation rings of modules over a certain class of symmetric algebras of finite representation type

Abstract

Let $\mathbf{k}$ be an algebraically closed field. Recently, K. Erdmann classified the symmetric $\mathbf{k}$-algebras $\Lambda$ of finite representation type such that every non-projective module $M$ has period dividing four. The goal of this paper is to determine the indecomposable modules $M$ over these class of algebras $\Lambda$ whose stable endomorphism ring is isomorphic to $\mathbf{k}$, and then calculate their corresponding universal deformation rings (in the sense of F. M. Bleher and the third author).