Simple Z-graded domains of Gelfand-Kirillov dimension two

[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.

[发布日期] 2020-11-15

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