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

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Velez-Marulanda, Jose A.¹ 

[1] Valdosta State Univ, Dept Math, Valdosta, GA 31698 USA

关键词: (Uni)versal deformation rings;    Finitely generated;    Gorenstein-projective modules;    Nakayama algebras;    Triangular matrix algebras;   

DOI  :  10.1016/j.jpaa.2020.106562

来源: Elsevier

【 摘 要 】

Let k be a fixed field of arbitrary characteristic and let Lambda 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 Lambda-module, then the versal deformation ring R(Lambda, 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 Sigma = (GRAPHICS) be a triangular matrix finite dimensional Gorenstein k-algebra with B projective as a left Lambda-module and with Gamma of finite global dimension. If ((V)(W))(f) is a finitely generated Gorenstein-projective left Sigma-module with f End(Sigma) (((V)(W))(f)) = k, then V is also a finitely generated Gorenstein-projective left Lambda-module with End(Lambda)(V) = k, and the versal deformation rings R (Sigma, ((V)(W))(f)) and R(Lambda, V) are both universal and isomorphic. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free