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Some nilpotent Lie algebras of even dimension

Published online by Cambridge University Press:  17 April 2009

Craig Seeley
Craig Seeley
Affiliation:
Department of Mathematics IAS ANU GPO Box 4 Canberra ACT 2601, Australia
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Abstract

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For each even dimension greater than or equal to 8, an infinite family of 3-step nilpotent Lie algebras over ℂ is constructed. In dimension m, the family contains isomorphism classes parameterised locally by approximately m3/48 essential parameters.

One particular case is studied further to get some global information about the variety of all nilpotent Lie algebras of dimension 8. Using the results obtained here, and some known facts, it is shown that there is a component consisting of algebras not having minimal possible central dimensions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 1 , February 1992 , pp. 71 - 77
Copyright
Copyright © Australian Mathematical Society 1992

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