Jose A. Velez-Marulanda

Universal deformation rings of modules over Frobenius algebras

Abstract Let k be a field, and let Λ be a finite dimensional k-algebra. We prove that if Λ is a self-injective algebra, then every finitely generated Λ-module V whose stable endomorphism ring is isomorphic to k has a universal deformation ring R ( Λ , V ) which is a complete local commutative Noetherian k-algebra with residue field k. If Λ is also a Frobenius algebra, we show that R ( Λ , V ) is stable under taking syzygies. We investigate a particular Frobenius algebra Λ 0 of dihedral type, as introduced by Erdmann, and we determine R ( Λ 0 , V ) for every finitely generated Λ 0 -module V whose stable endomorphism ring is isomorphic to k.

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