Wide subcategories of d-cluster tilting subcategories.

A subcategory of an abelian category is wide if it is closed under sums, summands, kernels, cokernels, and extensions. Wide subcategories provide a significant interface between representation theory and combinatorics. If Φ is a finite dimensional algebra, then each functorially finite wide subcategory of mod(Φ) is of the form φ*(mod(Γ)) in an essentially unique way, where \Γ is a finite dimensional algebra and Φ φ → Γ is an algebra epimorphism satisfying Tor^Φ₁(Γ,Γ) = 0. Let F ⊆ mod (Φ) be a d-cluster tilting subcategory as defined by Iyama. Then F is a d-abelian category as defined by Jasso, and we call a subcategory of F wide if it is closed under sums, summands, d-kernels, d-cokernels, and d-extensions. We generalise the above description of wide subcategories to this setting: Each functorially finite wide subcategory of F is of the form φ*(G) in an essentially unique way, where Φ φ → Γ is an algebra epimorphism satisfying Tor^Φ_d(Γ,Γ) = 0, and G ⊆ mod (\Gamma) is a d-cluster tilting subcategory. We illustrate the theory by computing the wide subcategories of some d-cluster tilting subcategories F ⊆ mod (Φ) over algebras of the form Φ = kA_m/(rad kA_m)^l. [ABSTRACT FROM AUTHOR]