A Dichotomy for the Gelfand–Kirillov Dimensions of Simple Modules over Simple Differential Rings

被引：0
作者：
Ashish Gupta
Arnab Dey Sarkar
机构：
[1] Indian Institute of Science Education and Research Bhopal,Department of Mathematics
来源：
Algebras and Representation Theory | 2018年 / 21卷
关键词：
Simple module; Gelfand–Kirillov dimension; Simple ring; 16S32; 16D60; 16P90;
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学科分类号：
摘要：
The Gelfand–Kirillov dimension has gained importance since its introduction as a tool in the study of non-commutative infinite dimensional algebras and their modules. In this paper we show a dichotomy for the Gelfand–Kirillov dimension of simple modules over certain simple rings of differential operators. We thus answer a question of J. C. McConnell in Representations of solvable Lie algebras V. On the Gelfand-Kirillov dimension of simple modules. McConnell (J. Algebra 76(2), 489–493, 1982) concerning this dimension for a class of algebras that arise as simple homomorphic images of solvable lie algebras. We also determine the Gelfand–Kirillov dimension of an induced module.
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页码：579 / 587
页数：8
相关论文
共 4 条
[1]  
Brookes CJB(2000)Modules over crossed products of division ring with an Abelian group I J. Algebra 229 25-54
[2]  
Groves JRJ(2013)GK Dimensions of simple modules over K[X±1,σ] Comm. Algebra 41 2593-2597
[3]  
Gupta A(1982)Representations of solvable Lie algebras. V. On the Gelfand-Kirillov dimension of simple modules J. Algebra 76 489-493
[4]  
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