Representations of solvable Lie algebras. V: On the Gelfand-Kirillov dimension of simple modules. (English) Zbl 0484.16013
MSC:
16P60 | Chain conditions on annihilators and summands: Goldie-type conditions |
17B35 | Universal enveloping (super)algebras |
16P40 | Noetherian rings and modules (associative rings and algebras) |
17B30 | Solvable, nilpotent (super)algebras |
16D30 | Infinite-dimensional simple rings (except as in 16Kxx) |
Keywords:
finitely generated algebra; faithful simple module; Gelfand-Kirillov dimension; Weyl algebra; Noetherian integral domains; enveloping algebras of solvable Lie algebrasCitations:
Zbl 0376.17003References:
[1] | Björk, J.-E, Rings of Differential Operators (1979), North-Holland: North-Holland Amsterdam/Oxford/New York · Zbl 0499.13009 |
[2] | Borho, W.; Kraft, H., Über die Gelfand-Kirillov Dimension, Math. Ann., 220, 1-24 (1976) · Zbl 0306.17005 |
[3] | Jacobson, N., Structure of Rings, (Colloquium Publications No. 37 (1956), Amer. Math. Soc: Amer. Math. Soc Providence, R.I) · JFM 65.1131.01 |
[4] | McConnell, J. C., Representations of solvable Lie algebras. II. Twisted group rings, Ann. Sci. Ecole Norm. Sup., 8, 156-178 (1975) · Zbl 0323.17006 |
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