2016•arXiv (Cornell University)Open access

A Dichotomy for GK dimensions of simple modules over simple differential rings

Ashish Gupta, Arnab Dey Sarkar

Abstract

The Gelfand--Kirillov dimension has gained importance since its introduction as an 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.

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Key concepts: Simple (philosophy), Dimension (graph theory), Mathematics, Differential (mechanical device), Pure mathematics, Simple module, Commutative property, Local ring