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

extAlgMultLie -- the (skew commutative) product in the Ext-algebra

Synopsis

Description

In the example below, ExtUL(QQ,QQ) is equal to R and a basis as a vector space is given by the generators of the ring representation L.cache.extAlgRing, see extAlgRing.

i1 : R=QQ[x,y,z, SkewCommutative=>{x,y,z}]

o1 = R

o1 : PolynomialRing
i2 : L=koszulDualLie(R)

o2 = L

o2 : LieAlgebra
i3 : extAlgLie 3

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

              3        3
o3 : Matrix ZZ  <--- ZZ
i4 : L.cache.extAlgRing

o4 = QQ[ext , ext , ext , ext , ext , ext , ext ]
           0     1     2     3     4     5     6

o4 : PolynomialRing
i5 : m=extAlgMultLie(ext_1,ext_2)

o5 = -ext
         3

o5 : QQ[ext , ext , ext , ext , ext , ext , ext ]
           0     1     2     3     4     5     6
i6 : extAlgMultLie(ext_0,m)

o6 = ext
        6

o6 : QQ[ext , ext , ext , ext , ext , ext , ext ]
           0     1     2     3     4     5     6

See also

Ways to use extAlgMultLie :