next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
GradedLieAlgebras :: dimTableLie

dimTableLie -- a table of dimensions of the Lie algebra in first and last degree

Synopsis

Description

The columns are referring to the degree, indexed from 1, and the rows are referring to the homological degree, indexed from 0. If the second argument s is zero (one), the dimensions of the even (odd) elements are displayed.

i1 : L=lieAlgebra({a,b,c,r3,r4},{},genWeights =>
          {{1,0},{1,0},{2,0},{3,1},{4,1}},
          genDiffs=>{[],[],[],{{1,-1},{[b,c],[a,c]}},
          {{1,-2},{[a,a,c],[b,b,b,a]}}},
          genSigns=>{1,1,0,0,1})

o1 = L

o1 : LieAlgebra
i2 : dimTableLie 5

o2 = | 2 4 4 7 16 |
     | 0 0 1 3 7  |
     | 0 0 0 0 0  |
     | 0 0 0 0 0  |
     | 0 0 0 0 0  |
     | 0 0 0 0 0  |

              6        5
o2 : Matrix ZZ  <--- ZZ
i3 : dimTableLie(5,0)

o3 = | 0 4 0 7 0 |
     | 0 0 1 0 7 |
     | 0 0 0 0 0 |
     | 0 0 0 0 0 |
     | 0 0 0 0 0 |
     | 0 0 0 0 0 |

              6        5
o3 : Matrix ZZ  <--- ZZ
i4 : dimTableLie(5,1)

o4 = | 2 0 4 0 16 |
     | 0 0 0 3 0  |
     | 0 0 0 0 0  |
     | 0 0 0 0 0  |
     | 0 0 0 0 0  |
     | 0 0 0 0 0  |

              6        5
o4 : Matrix ZZ  <--- ZZ

See also

Ways to use dimTableLie :