A178930 - OEIS

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

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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