A226951 Number of filiform Lie algebras with a certain grading of dimension n over Z_2.

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, 74, 60, 82, 64, 84, 68, 86, 74, 100, 84, 106, 92, 114, 98, 126, 104, 126, 112, 138, 122, 156, 134, 152, 140, 170, 142, 172, 152, 194, 176, 188, 170, 222, 196, 232, 184

Offset

4,3

Comments

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.

Links

John Tsartsaflis, Table of n, a(n) for n = 4..254

Grant Cairns, Ana Hinić Galić, and Yuri Nikolayevsky, Totally geodesic subalgebras of nilpotent Lie algebras, arxiv.org 1112.1288

John Tsartsaflis, Maple implementation

M. Vergne, Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes, Bull. Soc. Math. France 98 (1970), 81-116.

Crossrefs

Sequence in context: A164798 A087554 A281072 * A251557 A231901 A135974

Adjacent sequences: A226948 A226949 A226950 * A226952 A226953 A226954

Keyword

nonn

Author

John Tsartsaflis, Jun 24 2013

Status

approved