Fibers in Ore extensions
نویسندگان
چکیده
LetR be a finitely generated commutative algebra over an algebraically closed field k and let A = R[t;σ, δ] be the Ore extension with respect to an automorphism σ and a σ-derivation δ. We view A as the coordinate ring of an affine non-commutative space X. The inclusion R → A gives an affine map ξ : X → SpecR, and X is a non-commutative analogue of A 1 ×SpecR. We define the fiber Xp of ξ over a closed point p ∈ SpecR as a certain full subcategory ModXp of ModA. The category ModXp has the following structure. If p has infinite σ-orbit, then ModXp is equivalent to the category of graded modules over the polynomial ring k[x] with deg x = 1. If p is not fixed by σ, but has finite σ-orbit, say of size n, then ModXp is equivalent to the representations of the quiver Ãn−1 with the arrows all going in the same direction. If p is fixed by σ then ModXp is equivalent to either Modk or Modk[x]. It is also shown that X is the disjoint union of the fibers Xp in a certain sense.
منابع مشابه
Ore extensions of skew $pi$-Armendariz rings
For a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-Armendariz ring, that is a generalization of both $pi$-Armendariz rings, and $(alpha,delta)$-compatible skew Armendariz rings. We first observe the basic properties of skew $pi$-Armendariz rings, and extend the class of skew $pi$-Armendariz rings through various ring extensions. We nex...
متن کاملDouble Ore Extensions versus Iterated Ore Extensions
Motivated by the construction of new examples of Artin-Schelter regular algebras of global dimension four, J.J.Zhang and J.Zhang (2008) introduced an algebra extension AP [y1, y2;σ, δ, τ ] of A, which they called a double Ore extension. This construction seems to be similar to that of a two-step iterated Ore extension over A. The aim of this paper is to describe those double Ore extensions whic...
متن کاملPseudo linear transformations and evaluation in Ore extensions
The relations between evaluation of Ore polynomials and pseudo-linear transformations are studied. The behavior of these transformations under homomorphisms of Ore extensions, in particular with respect to algebraicity, is analyzed leading to characterization of left and right primitivity of an Ore extension. Necessary and sufficient conditions are given for algebraic pseudo-linear transformati...
متن کامل2 5 O ct 2 00 4 ORE EXTENSIONS OVER DUO RINGS
We show that there exist noncommutative Ore extensions in which every right ideal is two-sided. This answers a problem posed by Marks in [5]. We also provide an easy construction of one sided duo rings.
متن کامل