Simple Z-graded domains of Gelfand-Kirillov dimension two

JOURNAL OF ALGEBRA

卷:562

Article

Ferraro, Luigi¹  Gaddis, Jason²  Won, Robert³ 

[1] Wake Forest Univ, Dept Math & Stat, POB 7388, Winston Salem, NC 27109 USA

[2] Miami Univ, Dept Math, 301 S Patterson Ave, Oxford, OH 45056 USA

[3] Univ Washington, Dept Math, Box 354350, Seattle, WA 98195 USA

关键词: Generalized Weyl algebras;    Graded rings;    Noncommutative projective schemes;    Translation principle;    Morita equivalence;   

DOI  :  10.1016/j.jalgebra.2020.06.030

来源: Elsevier

【 摘 要 】

Let k be an algebraically closed field and A a Z-graded finitely generated simple k-algebra which is a domain of Gelfand-Kirillov dimension 2. We show that the category of Z-graded right A-modules is equivalent to the category of quasicoherent sheaves on a certain quotient stack. The theory of these simple algebras is closely related to that of a class of generalized Weyl algebras (GWAs). We prove a translation principle for the noncommutative schemes of these GWAs, shedding new light on the classical translation principle for the infinite-dimensional primitive quotients of U(sl(2)). (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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