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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lie algebras with finite Gelfand-Kirillov dimension


Authors: David Riley and Hamid Usefi
Journal: Proc. Amer. Math. Soc. 133 (2005), 1569-1572
MSC (2000): Primary 17B05, 16P90
Published electronically: January 13, 2005
MathSciNet review: 2120270
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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.


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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: http://dx.doi.org/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
Published electronically: January 13, 2005
Additional Notes: The research of the first author was supported by NSERC of Canada
Communicated by: Martin Lorenz
Article copyright: © Copyright 2005 American Mathematical Society