Functors

HomToIntegers
HomToIntegers(X)

Inputs either a ZG-resolution X=R, or an equivariant chain map X = (F:R \longrightarrow S). It returns the cochain complex or cochain map obtained by applying HomZG( _ , Z) where Z is the trivial module of integers (characteristic 0).
HomToIntegersModP
HomToIntegersModP(R)

Inputs a ZG-resolution R and returns the cochain complex obtained by applying HomZG( _ , Z_p) where Z_p is the trivial module of integers mod p. (At present this functor does not handle equivariant chain maps.)
HomToIntegralModule
HomToIntegralModule(R,f)

Inputs a ZG-resolution R and a group homomorphism f:G \longrightarrow GL_n(Z) to the group of n×n invertible integer matrices. Here Z must have characteristic 0. It returns the cochain complex obtained by applying HomZG( _ , A) where A is the ZG-module Z_n with G action via f. (At present this function does not handle equivariant chain maps.)
HomToGModule
HomToGModule(R,A)

Inputs a ZG-resolution R and an abelian G-outer group A. It returns the G-cocomplex obtained by applying HomZG( _ , A). (At present this function does not handle equivariant chain maps.)
LowerCentralSeriesLieAlgebra
LowerCentralSeriesLieAlgebra(G)
LowerCentralSeriesLieAlgebra(f)

Inputs a pcp group G. If each quotient G_c/G_{c+1} of the lower central series is free abelian or p-elementary abelian (for fixed prime p) then a Lie algebra L(G) is returned. The abelian group underlying L(G) is the direct sum of the quotients G_c/G_{c+1} . The Lie bracket on L(G) is induced by the commutator in G. (Here G_1=G, G_{c+1}=[G_c,G] .)

The function can also be applied to a group homomorphism f: G \longrightarrow G' . In this case the induced homomorphism of Lie algebras L(f):L(G) \longrightarrow L(G') is returned.

If the quotients of the lower central series are not all free or p-elementary abelian then the function returns fail.

This function was written by Pablo Fernandez Ascariz
TensorWithIntegers
TensorWithIntegers(X)

Inputs either a ZG-resolution X=R, or an equivariant chain map X = (F:R \longrightarrow S). It returns the chain complex or chain map obtained by tensoring with the trivial module of integers (characteristic 0).
TensorWithIntegersModP
TensorWithIntegersModP(X,p)

Inputs either a ZG-resolution X=R, or an equivariant chain map X = (F:R \longrightarrow S), and a prime p. It returns the chain complex or chain map obtained by tensoring with the trivial module of integers modulo p.
TensorWithRationals
TensorWithRationals(R)

Inputs a ZG-resolution R and returns the chain complex obtained by tensoring with the trivial module of rational numbers.