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Lie algebras with finite Gelfand-Kirillov dimension
Author(s):
David
Riley;
Hamid
Usefi
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1569-1572.
MSC (2000):
Primary 17B05, 16P90
Posted:
January 13, 2005
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Abstract:
We prove that every finitely generated Lie algebra containing a nilpotent ideal of class  and finite codimension  has Gelfand-Kirillov dimension at most  . In particular, finitely generated virtually nilpotent Lie algebras have polynomial growth.
References:
-
- 1.
- R.K. Amayo and I.N. Stewart, Finitely generated Lie algebras, J. London Math. Soc. 5 (1972), 697-703. MR 0323850 (48:2205)
- 2.
- Yu.A. Bahturin, Identical relations in Lie algebras (VNU Science Press, Utrecht, 1987). MR 0886063 (88f:17032)
- 3.
- A. Berele, Homogenous polynomial identities, Israel J. Math 42 (1982), 258-272. MR 0687131 (84b:16018)
- 4.
- M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. IHES 53 (1981), 53-73. MR 0623534 (83b:53041)
- 5.
- V.G. Kac, Simple irreducible graded Lie algebras of finite growth (in Russian), Math. USSR - Izvestija 2 (1968), 1271-1311. MR 0259961 (41:4590)
- 6.
- S. Kobayashi and M. Sanami, Growth of two-step solvable Lie algebras, Proc. Amer. Math. Soc. 109 (1990), no. 4, 859-863. MR 1015681 (91d:17011)
- 7.
- A.I. Lichtman, Growth in enveloping algebras, Israel J. Math. 47 (1984), no. 4, 296-304. MR 0764299 (86b:17008)
- 8.
- A.I. Lichtman and V.A. Ufnarovski, On growth of Lie algebras, Algebra Colloq. 2 (1995), no. 1, 45-49. MR 1314454 (95m:17002)
- 9.
- V.M. Petrogradsky, Intermediate growth in Lie algebras and their enveloping algebras, J. Algebra 179 (1996), no. 2, 459-482. MR 1367858 (96m:17018)
- 10.
- A. Shalev, Simple Lie algebras and Lie algebras of maximal class, Arch. Math. 63 (1994), 297-301. MR 1290602 (95j:17025)
- 11.
- A.L. Shmelkin, Free polynilpotent groups, Soviet Math. Dokl. 7 (1966), 1060-1061.
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Additional Information:
David
Riley
Affiliation:
Department of Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7
Email:
dmriley@uwo.ca
Hamid
Usefi
Affiliation:
Department of Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7
Email:
husefi@uwo.ca
DOI:
10.1090/S0002-9939-05-07618-5
PII:
S 0002-9939(05)07618-5
Received by editor(s):
August 27, 2003
Received by editor(s) in revised form:
December 9, 2003
Posted:
January 13, 2005
Additional Notes:
The research of the first author was supported by NSERC of Canada
Communicated by:
Martin Lorenz
Copyright of article:
Copyright
2005,
American Mathematical Society
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