Exercise 1, § 13

Tag 018U, permanent. Cite it as [Bourbaki, Tag 018U].

Lie Groups and Lie Algebras, VIII, 266

The dimensions $\leq 80$ of splittable simple Lie algebras are:

3 (A_1= B_1= C_1), 8 (A_2), 10 (B_2= C_2), 14 (G_2), 15 (A_3= D_3), 21 (B_3

and $C_3), 24 (A_4), 28 (D_4), 35 (A_5), 36 (B_4$ and $C_4), 45 (D_5), 48 (A_6), 52$ $(F_4), 55 (B_5$ and $C_5), 63 (A_7), 66 (D_6), 78 (B_6,C_6$ and $E_6), 80 (A_8)$ .

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