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

Author

Andrew Rupinski, Jan 11 2011

Keywords

• nonn

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?

Examples

			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