[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)
larmor.nuigalway.ie/~detinko/Csaba.pdf<http://larmor.nuigalway.ie/%7Edetinko/Csaba.pdf>
,
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:
http://list.seqfan.eu/pipermail/seqfan/2008-October/000002.html.
LEJ
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