basisExtLie -- a basis in a given degree of the Ext-algebra

Synopsis

• Usage:

  b = basisExtLie d

  b = basisExtLie(d1, d2)

  b = basisExtLie(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 list of basis elements

Description

i1 : L=lieAlgebra({a,b},{[a,a,b],[b,b,a]})

o1 = L

o1 : LieAlgebra

i2 : basisExtLie(3,2)

o2 = {ext , ext }
         2     3

o2 : List

i3 : extAlgLie 3

o3 = | 2 0 0 |
     | 0 0 2 |
     | 0 0 0 |

              3        3
o3 : Matrix ZZ  <--- ZZ

i4 : L.cache.extAlgRing

o4 = QQ[ext , ext , ext , ext ]
           0     1     2     3

o4 : PolynomialRing

See also

• signExtLie -- returns the sign of a generator in the Ext-algebra
• extAlgRing -- the ring representation of the Ext-algebra
• extAlgLie -- the matrix of dimensions of the Ext-algebra