[seqfan] On the number of unique isomorphism classes of nilpotent Lie algebras.

Ed Jeffery lejeffery7 at gmail.com
Sun Jul 1 07:06:03 CEST 2012

There is the beginning of an interesting sequence (apparently not in OEIS),
defined in (the presentation)


by Csaba Schneider, giving the number of unique isomorphism classes of
n-dimensional nilpotent Lie algebras, for n = 1, ..., 5. According to
Schneider, the sequence starts as

{1, 1, 2, 3, 9, ...}.

It is obviously going to be hard to extend this sequence since, for n >= 6,
one has to choose between the field characteristic being = 2 or <> 2, and
then it seems that the type of field also comes into play. I don't know
what restrictions can be imposed for all n to get the next finite term,
since there are several possible continuations, but it doesn't seem to be
such a simple generalization as for the first five terms. These
complications are reminiscent of those arising in Tanya Khovanova's tough
(and nice) sequence suggestion from Oct 25 2008:



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