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ideals_and_subalgebras.md

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CurrentModule = Oscar
DocTestSetup = Oscar.doctestsetup()

Ideals and Lie subalgebras

Ideals and Lie subalgebras are represented by the types LieAlgebraIdeal and LieSubalgebra respectively. They are used similarly in most cases.

Functions

Ideals

dim(::LieAlgebraIdeal)
basis(::LieAlgebraIdeal)
basis(::LieAlgebraIdeal, ::Int)
Base.in(::LieAlgebraElem, ::LieAlgebraIdeal)
bracket(::LieAlgebraIdeal{C,LieT}, ::LieAlgebraIdeal{C,LieT}) where {C<:FieldElem,LieT<:LieAlgebraElem{C}}
normalizer(::LieAlgebra, ::LieAlgebraIdeal)
centralizer(::LieAlgebra, ::LieAlgebraIdeal)

Lie subalgebras

dim(::LieSubalgebra)
basis(::LieSubalgebra)
basis(::LieSubalgebra, ::Int)
Base.in(::LieAlgebraElem, ::LieSubalgebra)
bracket(::LieSubalgebra{C,LieT}, ::LieSubalgebra{C,LieT}) where {C<:FieldElem,LieT<:LieAlgebraElem{C}}
normalizer(::LieAlgebra, ::LieSubalgebra)
centralizer(::LieAlgebra, ::LieSubalgebra)
is_self_normalizing(S::LieSubalgebra)

Constructors

Ideals

ideal(::LieAlgebra, ::Vector; is_basis::Bool=false)
ideal(::LieAlgebra{C}, ::LieAlgebraElem{C}) where {C<:FieldElem}
ideal(::LieAlgebra)

Lie subalgebras

sub(::LieAlgebra, ::Vector; is_basis::Bool=false)
sub(::LieAlgebra{C}, ::LieAlgebraElem{C}) where {C<:FieldElem}
sub(::LieAlgebra)

Conversions

lie_algebra(::LieSubalgebra)
lie_algebra(::LieAlgebraIdeal)
sub(::LieAlgebra{C}, ::LieAlgebraIdeal{C}) where {C<:FieldElem}