On weak universal deformation rings for objects of Ext-finite categories of modules
Abstract
Abstract Let $$\Lambda $$ Λ be a $$\mathbb {k}$$ k -algebra where $$\mathbb {k}$$ k is a field of arbitrary characteristic, and let $$\mathscr {A}_\mathbb {k}$$ A k be a full subcategory of $$\Lambda $$ Λ -Mod, the abelian category of left $$\Lambda $$ Λ -modules. In particular, $$\mathscr {A}_\mathbb {k}$$ A k is a $$\mathbb {k}$$ k -category, i.e. the set of morphisms between objects in $$\mathscr {A}_\mathbb {k}$$ A k is a vector space over $$\mathbb {k}$$ k and the composition of morphisms is $$\mathbb {k}$$ k -bilinear. Following M. Kleiner and I. Reiten, $$\mathscr {A}_\mathbb {k}$$ A k is Hom-finite if the hom-space between any two objects in $$\mathscr {A}_\mathbb {k}$$ A k is finite-dimensional over $$\mathbb {k}$$ k . We further say that $$\mathscr {A}_\mathbb {k}$$ A k is Ext-finite if $$\dim _\mathbb {k}\textrm{Ext}^i_\Lambda (X,Y)
Fields of Study & Subjects
Rings
Modules
and Algebras
Advanced Theoretical and Applied Studies in Material Sciences and Geometry
Publication details
- Journal / source
- Ricerche di Matematica
- Publisher
- Springer Science and Business Media LLC
- Volume
- 75
- Issue
- 4
- Pages
- 2303–2313
- Publication date
- 24 April 2026
- Language
- EN