login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A263005 Dimensions of the simple Lie algebras over complex numbers (with repetitions), sorted nondecreasingly. 0
3, 8, 10, 14, 15, 21, 21, 24, 28, 35, 36, 36, 45, 48, 55, 55, 57, 63, 66, 78, 78, 78, 80, 91, 99, 105, 105, 120, 120, 133, 136, 136, 143, 153, 168, 171, 171, 190, 195, 210, 210, 224, 231, 248, 253, 253, 255, 276, 288, 300, 300 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

The dimension duplications occur for the B_l and C_l series for l >= 3.

REFERENCES

E. Cartan, Sur la structure des groupes de transformation finis et continus. Thèse Paris 1894. Oeuvres Complètes, I,1, pp. 137-287, Paris 1952.

J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1972.

LINKS

Table of n, a(n) for n=1..51.

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: I, II, III, IV.

Hans Samelson, Notes on Lie Algebras.

CROSSREFS

Cf. A104599, A121214, A121732, A121736, A121737, A121738, A121739, A121741.

Sequence in context: A287573 A122529 A137920 * A126581 A003038 A184870

Adjacent sequences:  A263002 A263003 A263004 * A263006 A263007 A263008

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 23 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 24 01:41 EDT 2021. Contains 346269 sequences. (Running on oeis4.)