A178930 Number of semisimple Lie algebras of dimension n.

0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 3, 5, 3, 4, 8, 4, 5, 8, 7, 8, 11, 10, 11, 12, 13, 15, 19, 16, 21, 24, 21, 24, 32, 27, 34, 43, 37, 39, 53, 47, 54, 65, 65, 68, 79, 80, 90, 98, 102, 114, 129, 122, 138, 160, 157, 172, 207, 193, 211, 247, 244, 262, 306, 305, 329, 363, 378, 399, 448, 460

Offset

0,15

Comments

a(n) is also the number of simply-connected semisimple Lie groups.

Is a(n) eventually monotonically increasing, and if so, beyond what index?

Links

Table of n, a(n) for n=0..79.

Example

a(3) = 1 since A_1 is the only semisimple Lie algebra of dimension 3.
For n=21, the a(21) = 5 such Lie algebras are A_1+A_1+A_1+A_1+A_1+A_1+A_1, A_1+A_1+A_3, A_1+A_2+B_2, B_3, and C_3

Crossrefs

Sequence in context: A366580 A088019 A301508 * A126759 A293444 A302791

Adjacent sequences: A178927 A178928 A178929 * A178931 A178932 A178933

Keyword

nonn

Author

Andrew Rupinski, Jan 11 2011

Status

approved