On Deformations of Gorenstein-Projective Modules over Monomial Algebras with no Overlaps

Abstract

Let $\mathbf{k}$ be a field of arbitrary characteristic, let $\Lambda$ be a finite dimensional $\mathbf{k}$-algebra, and let $V$ be an indecomposable Gorenstein-projective $\Lambda$-module with finite dimension over $\mathbf{k}$. It follows that $V$ has a well-defined versal deformation ring $R(\Lambda, V)$, which is complete local commutative Noetherian $\mathbf{k}$-algebra with residue field $\mathbf{k}$, and which is universal provided that the stable endomorphism ring of $V$ is isomorphic to $\mathbf{k}$. We prove that if $\Lambda$ is a monomial algebra without overlaps, then $R(\Lambda,V)$ is universal and isomorphic either to $\mathbf{k}$ or to $\mathbf{k}[[t]]/(t^2)$