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GradedLieAlgebras :: RingElement RingElement

RingElement RingElement -- Multiplication in the Ext-algebra

Synopsis

Description

The elements x and y are linear polynomials in L.cache.extRepRing and z is the product in the skewcommutative algebra ExtUL(k,k) where k is L.field.

i1 : L = lieAlgebra({a,b,c},genSigns=>1)/{a a,b c,a b+c c}

o1 = L

o1 : LieAlgebra
i2 : extBasisLie 4

o2 = {ext , ext , ext , ext , ext , ext , ext , ext , ext }
         0     1     2     3     4     5     6     7     8

o2 : List
i3 : extTableLie 4

o3 = | 3 0 0 0 |
     | 0 3 0 0 |
     | 0 0 1 1 |
     | 0 0 0 1 |

              4        4
o3 : Matrix ZZ  <--- ZZ
i4 : ext_0 ext_5

o4 = ext
        6

o4 : QQ[ext , ext , ext , ext , ext , ext , ext , ext , ext ]
           0     1     2     3     4     5     6     7     8
i5 : weightExtLie ext_6

o5 = {3, 3}

o5 : List

See also