A226951 - OEIS

%I #28 Feb 22 2014 04:01:48

%S 1,1,2,4,4,6,6,10,10,16,14,20,18,26,20,32,28,36,32,44,40,56,46,56,54,

%T 74,60,82,64,84,68,86,74,100,84,106,92,114,98,126,104,126,112,138,122,

%U 156,134,152,140,170,142,172,152,194,176,188,170,222,196,232,184

%N Number of filiform Lie algebras with a certain grading of dimension n over Z_2.

%C Let G = <X_1,X_2,...,X_n> be a filiform Lie algebra of dimension n over Z_2. Define the grading [X_i,X_j]=c_(i,j)X_(i+j), for i,j >=2 for some constants c_(i,j) in Z_2. How many such algebras there exist on dimension n? The sequence gives us up to a point this numbers starting with dimension four, that is, there exists only one such an algebra with dimension four, 1 again with dimension 5, 2 with dimension 6 and so forth.

%H John Tsartsaflis, <a href="/A226951/b226951.txt">Table of n, a(n) for n = 4..254</a>

%H Grant Cairns, Ana Hinić Galić, and Yuri Nikolayevsky, <a href="http://arxiv.org/abs/1112.1288">Totally geodesic subalgebras of nilpotent Lie algebras</a>, arxiv.org 1112.1288

%H John Tsartsaflis, <a href="/A226951/a226951.mw.txt">Maple implementation</a>

%H M. Vergne, <a href="http://www.numdam.org/item?id=BSMF_1970__98__81_0">Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes</a>, Bull. Soc. Math. France 98 (1970), 81-116.

%K nonn

%O 4,3

%A _John Tsartsaflis_, Jun 24 2013