Lie algebras with finite Gelfand-Kirillov dimension
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- by David Riley and Hamid Usefi PDF
- Proc. Amer. Math. Soc. 133 (2005), 1569-1572 Request permission
Abstract:
We prove that every finitely generated Lie algebra containing a nilpotent ideal of class $c$ and finite codimension $n$ has Gelfand-Kirillov dimension at most $cn$. In particular, finitely generated virtually nilpotent Lie algebras have polynomial growth.References
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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
- MR Author ID: 722015
- Email: husefi@uwo.ca
- Received by editor(s): August 27, 2003
- Received by editor(s) in revised form: December 9, 2003
- Published electronically: January 13, 2005
- Additional Notes: The research of the first author was supported by NSERC of Canada
- Communicated by: Martin Lorenz
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 1569-1572
- MSC (2000): Primary 17B05, 16P90
- DOI: https://doi.org/10.1090/S0002-9939-05-07618-5
- MathSciNet review: 2120270