Let k be a fixed algebraically closed field of arbitrary characteristic,let Λ be a finite dimensional self-injective k-algebra,and let ∨ be an indecomposable non-projective left Λ-module with finite dimension over ...Let k be a fixed algebraically closed field of arbitrary characteristic,let Λ be a finite dimensional self-injective k-algebra,and let ∨ be an indecomposable non-projective left Λ-module with finite dimension over k.We prove that if τΛ∨ is the Auslander-Reiten translation of ∨,then the versal deformation rings R(Λ,∨)and R(Λ,τΛ∨)(in the sense of F.M.Bleher and the second author)are isomorphic.We use this to prove that if Λ is further a cluster-tilted k-algebra,then R(Λ,∨)is universal and isomorphic to k.展开更多
基金supported by the Release Time for Research Scholarship of the Office of Academic Affairs and by the Faculty Research Seed Grant funded by the Office of Sponsored ProgramsResearch Administration at the Valdosta State University as well as partly supported by CODI and Estrategia de Sostenibilidad(Universidad de Antioquia,UdeA).
文摘Let k be a fixed algebraically closed field of arbitrary characteristic,let Λ be a finite dimensional self-injective k-algebra,and let ∨ be an indecomposable non-projective left Λ-module with finite dimension over k.We prove that if τΛ∨ is the Auslander-Reiten translation of ∨,then the versal deformation rings R(Λ,∨)and R(Λ,τΛ∨)(in the sense of F.M.Bleher and the second author)are isomorphic.We use this to prove that if Λ is further a cluster-tilted k-algebra,then R(Λ,∨)is universal and isomorphic to k.
