On deformations of Gorenstein-projective modules over Nakayama and triangular matrix algebras

Abstract

Let k be a fixed field of arbitrary characteristic and let Λ be a basic connected Nakayama k -algebra without simple projective modules. In this article we prove that if V is an indecomposable finitely generated Gorenstein-projective left Λ-module, then the versal deformation ring R ( Λ , V ) (in the sense of F. M. Bleher and the author) is universal and stable after taking syzygies . We also prove the following result. Let Σ = ( Λ B 0 Γ ) be a triangular matrix finite dimensional Gorenstein k -algebra with B projective as a left Λ-module and with Γ of finite global dimension. If ( V W ) f is a finitely generated Gorenstein-projective left Σ-module with End _ Σ ( ( V W ) f ) = k , then V is also a finitely generated Gorenstein-projective left Λ-module with End _ Λ ( V ) = k , and the versal deformation rings R ( Σ , ( V W ) f ) and R ( Λ , V ) are both universal and isomorphic.