Universal deformation rings of modules for generalized Brauer tree algebras of polynomial growth

Let k be an arbitrary field, Λ a k-algebra and V Λ-module. When it exists, the universal deformation ring R(Λ,V) of is whose local homomorphisms to R parametrize lifts up R⊗kΛ, where any complete, commutative Noetherian with residue field k. Symmetric special biserial algebras, which coincide Brauer graph can viewed as generalizing blocks finite type p-modular group algebras. Bleher Wackwitz classified rings for all modules symmetric algebras representation type. In this paper, we begin address tame case. Specifically, let 1-domestic, algebra. By viewing generalized tree making use derived equivalence, classify those Λ-modules stable endomorphism isomorphic The latter natural condition, since guarantees existence R(Λ,V).