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

RingElement LieElement -- Multiplication of a field element and a LieElement

Synopsis

Description

The symbol SPACE is used as notation for multiplication by scalars. The scalars belong to L.field. 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. If the field is not a prime field, then sometimes it is necessary to define the field outside the constructor lieAlgebra. Observe also 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]/ideal{x^2+1})

o1 = F

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

o2 = L

o2 : LieAlgebra
i3 : (3*x+2) a b + (2*x+3) b a

o3 = (-x+1)(b a)

o3 : L

See also