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A263005 Dimensions of the simple Lie algebras over complex numbers (with repetitions), sorted nondecreasingly.

%I A263005 #12 Oct 26 2015 04:17:03
%S A263005 3,8,10,14,15,21,21,24,28,35,36,36,45,48,55,55,57,63,66,78,78,78,80,
%T A263005 91,99,105,105,120,120,133,136,136,143,153,168,171,171,190,195,210,
%U A263005 210,224,231,248,253,253,255,276,288,300,300
%N A263005 Dimensions of the simple Lie algebras over complex numbers (with repetitions), sorted nondecreasingly.
%C A263005 This sequence gives the dimensions of the (compact) simple Lie algebras A_l, l >= 1, B_l, l >= 2, C_l >= 3, D_l, l >= 4, E_6, E_7, E_8, F_4 and G_2 which are l*(l+2), l*(2*l + 1), l*(2*l + 1), l*(2*l - 1), 78, 133, 248, 52 and 14, respectively. These are also the dimensions of the adjoint representations of these Lie algebras. For the l-ranges see the Humphreys reference, p. 58, and for the dimensions, e.g., the Samelson link, Theorem A, p. 74.
%C A263005 The dimension duplications occur for the B_l and C_l series for l >= 3.
%D A263005 E. Cartan, Sur la structure des groupes de transformation finis et continus. Thèse Paris 1894. Oeuvres Complètes, I,1, pp. 137-287, Paris 1952.
%D A263005 J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1972.
%H A263005 W. Killing, Die Zusammensetzung der stetigen endlichen Transformationsgruppen, Mathematische Ann. I: 31 (1888) 252-290, II: 33 (1889) 1-48, III: 34 (1889) 57-122, IV: 36 (1890) 161-189: <a href="https://eudml.org/doc/157352">I</a>, <a href="https://eudml.org/doc/157397">II</a>, <a href="https://eudml.org/doc/157434">III</a>, <a href="https://eudml.org/doc/157490">IV</a>.
%H A263005 Hans Samelson, <a href="http://www.math.cornell.edu/~hatcher/Other/Samelson-LieAlg.pdf">Notes on Lie Algebras</a>.
%Y A263005 Cf. A104599, A121214, A121732, A121736, A121737, A121738, A121739, A121741.
%K A263005 nonn,easy
%O A263005 1,1
%A A263005 _Wolfdieter Lang_, Oct 23 2015