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GradedLieAlgebras :: extBasisLie

extBasisLie -- a basis up to a given degree of the Ext-algebra

Synopsis

Description

This gives a basis (in positive degrees) up to the specified degree of ExtUL(k,k) where k=L.field or the basis in a specified first and last degree or multi-degree. The basis elements are the generators in the polynomial ring L.cache.extRepRing, see extRepRing.

i1 : L=lieAlgebra{a,b}/{a a b,b b a}

o1 = L

o1 : LieAlgebra
i2 : extBasisLie 4

o2 = {ext , ext , ext , ext , ext }
         0     1     2     3     4

o2 : List
i3 : extTableLie 4

o3 = | 2 0 0 0 |
     | 0 0 2 0 |
     | 0 0 0 1 |
     | 0 0 0 0 |

              4        4
o3 : Matrix ZZ  <--- ZZ
i4 : extBasisLie(3,2)

o4 = {ext , ext }
         2     3

o4 : List
i5 : weightExtLie(ext_2-3*ext_3)

o5 = {3, 2}

o5 : List
i6 : ext_2

o6 = ext
        2

o6 : QQ[ext , ext , ext , ext , ext ]
           0     1     2     3     4
i7 : signExtLie ext_2

o7 = 0

See also

Ways to use extBasisLie :