Singular equivalences of Morita type with level, Gorenstein algebras, and universal deformation rings

Let k be a field of arbitrary characteristic, let Λ be a finite dimensional k-algebra, and let V be an indecomposable finitely generated non-projective Gorenstein-projective left Λ-module whose stable endomorphism ring is isomorphic to k. In this article, we prove that the universal deformation rings R(Λ, V ) and R(Λ, ΩΛV ) are isomorphic, where ΩΛV denotes the first syzygy of V as a left Λ-module. We also prove the following result. Assume that Λ is also Gorenstein and that Γ is another Gorenstein k-algebra such that there exists ` ≥ 0 and a pair of bimodules (ΓXΛ, ΛYΓ) that induces a singular equivalence of Morita type with level ` (as introduced by Z. Wang) between Λ and Γ. Then the left Γ-module X ⊗Λ V is also Gorenstein-projective with stable endomorphism ring isomorphic to k, and the universal deformation ring R(Γ, X ⊗Λ V ) is isomorphic to R(Λ, V ).

• Autores: Vélez Marulanda, José Alberto
• Tipo de recurso: Article of investigation
• Fecha de publicación: 2023
• Institución: Universidad de Antioquia
• Repositorio: Repositorio UdeA
• Idioma: eng
• OAI Identifier: oai:bibliotecadigital.udea.edu.co:10495/46191
• Acceso en línea: https://hdl.handle.net/10495/46191
• Palabra clave: Anillos de Gorenstein; Gorenstein rings; Anillos de endomorfismo; Endomorphism rings; Equivalencias singulares de tipo Morita; Singular equivalences of Morita; http://id.loc.gov/authorities/subjects/sh93007380; http://id.loc.gov/authorities/subjects/sh85043085
• Rights: openAccess
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/