Noncommutative graded domains with quadratic growth

Abstract

Contents o. Introduction 1. The graded quotient ring of a graded prime ring of dimension two 2. The associated divisors 3. The stable image of the curve 4. Domains of dimension two which are generated in degree one 5. The case of an automorphism of infinite order 6. Applications to the structure of graded domains of dimension two 231 235 244 254 257 264 270

Noetherian hereditary abelian categories satisfying Serre duality

“…Hence by the properties of triangles we have h A = f g for a map f : B → τA [1]. This proves what we want.…”

“…If either of these properties holds, then the action of the Serre functor on objects coincides withτ [1].…”

“…It is shown in [14, §4.3] that given C the corresponding Auslander-Reiten triangle A → B → C → A [1] is unique up to isomorphism of triangles. (By duality a similar result holds if A is given.)…”

“…, and let h be a non-zero element of the socle of Hom(C,τ C [1]). We claim that the associated trianglẽ…”

PBW deformations of Artin–Schelter regular algebras

“…Artin and Stafford have shown that every domain of GK dimension two is isomorphic to a twisted homogeneous coordinate ring [1]. Hence, if H is 3-dimensional regular and g ∈ H 3 is a normal element which is not a zero-divisor, then H/gH must be isomorphic to some B.…”