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GradedLieAlgebras :: dimLie

dimLie -- the dimension of a Lie algebra

Synopsis

Usage:
a = dimLie(d)
a = dimLie(d1, d2)
a = dimLie(dl)
Inputs:
- d, an integer, the degree
- d1, an integer, the first degree
- d2, an integer, the last degree
- dl, a list, the multidegree
Outputs:
- a, an integer, the dimension in the specified degree.

Description

i1 : L=lieAlgebra({a,b,c},{[c,c,b]},genWeights=>{{2,1},{1,0},{1,0}},
         genDiffs=>{[b,c],[],[]},genSigns=>{1,0,0})

o1 = L

o1 : LieAlgebra

i2 : dimTableLie 4

o2 = | 2 1 1 1 |
     | 0 1 2 4 |
     | 0 0 0 1 |
     | 0 0 0 0 |
     | 0 0 0 0 |

              5        4
o2 : Matrix ZZ  <--- ZZ

i3 : dimLie 4

o3 = 6

i4 : dimLie(4,0)

o4 = 1

i5 : dimLie(4,1)

o5 = 4

i6 : dimLie({4,2})

o6 = 1

See also

dimtotLie -- the total dimension up to degree d
dimsLie -- the dimensions of a Lie algebra
dimTableLie -- a table of dimensions of the Lie algebra in first and last degree

Ways to use `dimLie` :

dimLie(List)
dimLie(ZZ)
dimLie(ZZ,ZZ)