new model for lie algebras

Author: vitktor

src/on_varieties/lie-symmetries/lie-algebras-new.jl

@@ -0,0 +1,38 @@
+abstract type AbstractLieAlgebra end
+
+struct LieAlgebra <: AbstractLieAlgebra
+
+end
+
+struct SumLieAlgebra <: AbstractLieAlgebra
+    algs::Vector{AbstractLieAlgebra}
+end
+
+
+abstract type AbstractLieAlgebraElem end
+
+struct LieAlgebraElem <: AbstractLieAlgebraElem
+    alg::LieAlgebra
+    coeffs::Vector{ComplexF64}
+end
+
+struct SumLieAlgebraElem <: AbstractLieAlgebraElem
+    alg::SumLieAlgebra
+    elems::Vector{AbstractLieAlgebraElem}
+end
+
+
+abstract type AbstractLieAlgebraAction end
+
+struct LieAlgebraAction <: AbstractLieAlgebraAction
+    alg::LieAlgebra
+    vars::Vector{Vector{Variable}}
+end
+
+struct SumLieAlgebraAction <: AbstractLieAlgebraAction
+    alg::SumLieAlgebra
+end
+
+struct ScalingLieAction <: AbstractLieAlgebraAction
+
+end

src/on_varieties/lie-symmetries/lie-algebras.jl

@@ -31,7 +31,7 @@ export LieAlgebra,
     irreducible_components,
     PolynomialVectorSpace,
     decompose,
-    ⊞
+    ⊞, ∩
 
 struct WeightStructure
     weights::Vector{Vector{Int}}
@@ -383,7 +383,7 @@ algebra(π::IrreducibleLieAlgebraRepresentation) = π.alg
 space_basis(π::IrreducibleLieAlgebraRepresentation) = basis(π.hw_module)
 highest_weight(π::IrreducibleLieAlgebraRepresentation) = highest_weight(π.hw_module)
 highest_weight_vector(π::IrreducibleLieAlgebraRepresentation) = highest_weight_vector(π.hw_module)
-dim(π::IrreducibleLieAlgebraRepresentation) = 2*highest_weight(π)[1]+1 # TODO: works only for so(3)
+dim(π::IrreducibleLieAlgebraRepresentation) = prod([2*j+1 for j in highest_weight(π)]) # TODO: works only for so(3)
 
 function to_expressions(π::IrreducibleLieAlgebraRepresentation; tol::Float64=1e-5)
     exprs = Expression[]