2024/01/13 by José A. Vélez-Marulanda, Velez-Marulanda, Jose A., Héctor Suárez +1
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2402.18580
Let k be a field of arbitrary characteristic, and let Λ be a finite dimensional k-algebra. In this short note we prove that if V is a finitely generated strongly Gorenstein-projective left Λ-module whose stable endomorphism ring \underlineEndΛ(V) is isomorphic to k, then V has an universal deformation ring R(Λ,V) isomorphic to the ring of dual numbers k[ε] with ε2=0. As a consequence, we obtain the following result. Assume that Q is a finite connected acyclic quiver, let k Q be the corresponding path algebra and let Λ= k Q[ε] = k Q⊗k k[ε]. If V is a finitely generated Gorenstein-projective left Λ-module with \underlineEndΛ(V)=k, then V has an universal deformation ring R(Λ,V) isomorphic to k[ε]