[seqfan] nilpotent lie algebras

Tanya Khovanova mathoflove-seqfan at yahoo.com
Sat Oct 25 15:56:31 CEST 2008

Hello SeqFans,

I found the following in my old notes from the lectures of A.A.Kirillov
on the representation theory:

All nilpotent Lie algebras in dimension 1 and 2 are abelian. Thus, for
dimensions 1 and 2 the number of irreducible nilpotent Lie algebras is
1 and 0 correspondingly.

In dimension 3 (also 4) there is only one irreducible nilpotent lie
algebra (corresponding to the Heisenberg group).

In dimension 5, the number is 6.
In dimension 6 - 23.
In dimension 7 a parameter appears and the number becomes a continuum.

I think there should be a sequence here, but I am not sure what to do
with continuum. Also, my notes are so old, that I would like someone to
confirm that the sequence indeed is: 1,0,1,1,6,23

Best, Tanya

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