Some Open Problems in the Context of Skew PBW Extensions and Semi-graded Rings  

作　　者：Oswaldo Lezama 

机构地区：[1]Seminario deÁlgebra Constructiva-SAC2,Departamento de Matemáticas,Universidad Nacional de Colombia,Sede Bogotá,Bogotá,Colombia

出　　处：《Communications in Mathematics and Statistics》2021年第3期347-378,共32页数学与统计通讯（英文）

摘　　要：In this paper,we discuss some open problems of non-commutative algebra and noncommutative algebraic geometry from the approach of skew PBW extensions and semi-graded rings.More exactly,we will analyze the isomorphism arising in the investigation of the Gelfand–Kirillov conjecture about the commutation between the center and the total ring of fractions of an Ore domain.The Serre’s conjecture will be discussed for a particular class of skew PBW extensions.The questions about the Noetherianity and the Zariski cancellation property of Artin–Schelter regular algebras will be reformulated for semi-graded rings.Advances for the solution of some of the problems are included.

关 键 词：Gelfand–Kirillov conjecture Serre’s conjecture Artin–Schelter regular algebras Zariski cancellation problem Skew PBW extensions Semi-graded rings 

分 类 号：O15[理学—数学]