A Dichotomy for GK dimensions of simple modules over simple differential rings
Ashish Gupta, Arnab Dey Sarkar
TL;DR
This paper establishes a clear dichotomy in the Gelfand--Kirillov dimensions of simple modules over specific simple rings of differential operators, advancing understanding in non-commutative algebra.
Contribution
It introduces a dichotomy result for GK dimensions of simple modules over certain simple differential rings, a novel insight in the field.
Findings
Identifies a dichotomy in GK dimensions for simple modules
Applicable to specific classes of simple differential rings
Enhances understanding of module structure in non-commutative algebra
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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Finite Group Theory Research