Smash products deformations

DeformationMap{T} = MatElem{T} where {T <: SmashProductLieElem}

The type for deformation maps of a Lie algebra smash product. The entry kappa[i,j] should be the image of $v_i \wedge v_j$ under the deformation map, i.e. $κ(v_i,v_j)$. Deformation maps are always assumed to be quadratic and skew-symmetric.

deform(sp::SmashProductLie{C}, kappa::DeformationMap{elem_type(sp)}) where {C <: RingElem}

Constructs the deformation of the smash product sp by the deformation map kappa.

Returns a SmashProductLieDeform struct and a two-part basis.

symmetric_deformation(sp::SmashProductLie{C}) where {C <: RingElem}

Constructs the symmetric deformation of the smash product sp.

The struct representing a deformation of a Lie algebra smash product. It consists of the underlying FreeAssociativeAlgebra with relations and some metadata. It gets created by calling deform.