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A001066 Dimensions (sorted, with duplicates removed) of real simple Lie algebras. 4
3, 6, 8, 10, 14, 15, 16, 20, 21, 24, 28, 30, 35, 36, 42, 45, 48, 52, 55, 56, 63, 66, 70, 72, 78, 80, 90, 91, 96, 99, 104, 105, 110, 120, 126, 132, 133, 136, 143, 153, 156, 160, 168, 171, 182, 190, 195, 198, 210, 224, 231, 240, 248, 253, 255, 266, 272, 276, 286, 288, 300, 306 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The possible dimensions of real simple Lie algebras are the numbers n and 2n where n runs through the dimensions of the complex simple Lie algebras.

REFERENCES

Freeman J. Dyson, Missed opportunities, Bull. Amer. Math. Soc. 78 (1972), 635-652.

N. Jacobson, Lie Algebras. Wiley, NY, 1962; see pp. 141-146.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

Numbers n and 2n as n runs through A003038.

EXAMPLE

6 is the dimension of the real simple Lie algebra SL_2(C).

MATHEMATICA

max = 18; sa = Table[k*(k+2), {k, 1, max}]; sb = Table[k*(2k+1), {k, 2, max}]; sd := Table[k*(2k-1), {k, 4, max}]; se = {14, 52, 78, 133, 248}; Select[ Union[sa, 2*sa, sb, 2*sb, sd, 2*sd, se, 2*se], # <= max^2 &] (* Jean-Fran├žois Alcover, Apr 02 2012, after A003038 *)

PROG

(Haskell)

import Data.Set (deleteFindMin, fromList, insert)

a001066 n = a001066_list !! (n-1)

a001066_list = f (fromList [h, 2 * h]) $ tail a003038_list where

   h = head a003038_list

   f s (x:xs) = m : f (x `insert` (( 2 * x) `insert` s')) xs where

     (m, s') = deleteFindMin s

-- Reinhard Zumkeller, Dec 16 2012

CROSSREFS

Cf. A003038.

Subsequences, apart from some initial terms: A000217, A000384, A002378, A005563, A014105.

Sequence in context: A064437 A287180 A072149 * A099518 A280106 A184855

Adjacent sequences:  A001063 A001064 A001065 * A001067 A001068 A001069

KEYWORD

nonn,nice,easy

AUTHOR

Richard E. Borcherds (reb(AT)math.berkeley.edu)

EXTENSIONS

Entry revised by N. J. A. Sloane, Mar 16 2007

STATUS

approved

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Last modified January 26 14:08 EST 2020. Contains 331280 sequences. (Running on oeis4.)