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- Title
A Dichotomy for the Gelfand-Kirillov Dimensions of Simple Modules over Simple Differential Rings.
- Authors
Gupta, Ashish; Sarkar, Arnab Dey
- Abstract
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.
- Publication
Algebras & Representation Theory, 2018, Vol 21, Issue 3, p579
- ISSN
1386-923X
- Publication type
Article
- DOI
10.1007/s10468-017-9728-6