Smash products deformations
Constructors
PBWDeformations.DeformationMap
— TypeDeformationMap{C} = MatElem{FreeAssAlgElem{C}} where {C <: RingElem}
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.
PBWDeformations.deform
— Functiondeform(sp::SmashProductLie{C}, kappa::DeformationMap{C}) 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.
PBWDeformations.symmetric_deformation
— Functionsymmetric_deformation(sp::SmashProductLie{C}) where {C <: RingElem}
Constructs the symmetric deformation of the smash product sp
.
SmashProductLieDeform struct
PBWDeformations.SmashProductLieDeform
— TypeThe struct representing a deformation of a Lie algebra smash product. It consists of the underlying FreeAssAlgebra with relations and some metadata. It gets created by calling deform
.
Functions
The SmashProductLieDeform
struct can be used as an argument for the following functions:
gen
gens
ngens
For gen
, gens
, and ngens
, on can supply a symbol to choose the part of the smash product to use: :L
for the Lie algebra, and :V
for the module.