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GradedLieAlgebras :: RingElement ExtElement

RingElement ExtElement -- multiplication of a field element and a Ext-algebra element



The symbol SPACE is used as notation for multiplication by scalars. The scalars belong to the field of $E$. If the field is not QQ, then the scalars are of type RingElement. If the field is QQ, then the scalars are of type Number. Observe that it is necessary to use the function toField when $F$ is defined as an algebraic extension of a prime field.

i1 : F = toField(ZZ/7[x]/{x^2+1})

o1 = F

o1 : PolynomialRing
i2 : L = lieAlgebra({a,b,c},Field=>F)/{a b,b c}

o2 = L

o2 : LieAlgebra
i3 : E = extAlgebra(3,L)

o3 = E

o3 : ExtAlgebra
i4 : (3*x+1) (ext_1 ext_2)+(2*x+3) (ext_2 ext_1)

o4 = (-x+2)ext_3

o4 : E

See also