basisLie -- a basis of Lie monomials in a given (multi-)degree

Synopsis

• Usage:

  b = basisLie(d)

  b = basisLie(d1, d2)

  b = basisLie(dl)

• Inputs:

  • d, an integer, the degree
  • d1, an integer, the first degree
  • d2, an integer, the last degree = the homological degree
  • dl, a list, the multidegree
• Outputs:

  • b, a list, the basis, a list of Lie monomials

Description

i1 : L=lieAlgebra({x,y},{},genSigns=>{1,0},genWeights=>{{2,0},{2,1}},
         genDiffs=>{[],[x]},field=>ZZ/3)

o1 = L

o1 : LieAlgebra

i2 : dimTableLie 4

o2 = | 0 1 0 1 |
     | 0 1 0 1 |
     | 0 0 0 0 |
     | 0 0 0 0 |
     | 0 0 0 0 |

              5        4
o2 : Matrix ZZ  <--- ZZ

i3 : basisLie 4

o3 = {[x, x], [y, x]}

o3 : List

i4 : basisLie{4,1}

o4 = {[y, x]}

o4 : List

i5 : basisLie(4,0)

o5 = {[x, x]}

o5 : List

See also

• dimLie -- the dimension of a Lie algebra
• basisExtLie -- a basis in a given degree of the Ext-algebra
• indexFormLie -- returns an element in the ring representation corresponding to the input
• basicMonomialLie -- checks if an array is a basis element for the Lie algebra