On a Deformation Theory of Finite Dimensional Modules Over Repetitive Algebras

Let Λ be a basic finite dimensional algebra over an algebraically closed field k, and let Λ be the repetitive algebra of Λ. In this article, we prove that if V is a left Λ-module with finite dimension b over k, then V has a well-defined versal deformation ring R(Λ, V), which is a local complete Noetherian commutative k-algebra whose residue field is also isomorphic to k. We also prove that R(Λb, Vb) is universal provided that EndΛ (V) = k and that in this situation, R(Λb, Vb) is stable after taking syzygies. We apply the obtained results to finite dimensional modules over the repetitive algebra of the 2-Kronecker algebra, which provides an alternative approach to the deformation theory of objects in the bounded derived category of coherent sheaves over P 1 k.

• Autores: Hernández Rizzo, Pedro Jesús; Giraldo Salazar, Hernán Alonso; Fonce Camacho, Adriana Marcela; Vélez Marulanda, José Alberto
• Tipo de recurso: Article of investigation
• Fecha de publicación: 2021
• Institución: Universidad de Antioquia
• Repositorio: Repositorio UdeA
• Idioma: eng
• OAI Identifier: oai:bibliotecadigital.udea.edu.co:10495/46312
• Acceso en línea: https://hdl.handle.net/10495/46312; https://doi.org/10.1007/s10468-021-10083-5
• Palabra clave: Anillos (Álgebra); Rings (algebra); Álgebra conmutativa; Commutative algebra; Modulos (Álgebra); Modules (Algebra)
• Rights: openAccess
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/