A dichotomy for the Gelfand-Kirillov dimensions of simple modules over simple differential rings. (English) Zbl 1427.16015
Summary: 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 [J. Algebra 76, 489–493 (1982; Zbl 0484.16013)] 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.
MSC:
| 16P90 | Growth rate, Gelfand-Kirillov dimension |
| 16S32 | Rings of differential operators (associative algebraic aspects) |
| 16D60 | Simple and semisimple modules, primitive rings and ideals in associative algebras |
Citations:
Zbl 0484.16013References:
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