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 | References | Similar Articles | Additional Information

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.

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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

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