Merge branch 'kellertuer/first-group' of github.com:JuliaManifolds/Li…

…eGroups.jl into kellertuer/first-group
JuliaManifolds · Oct 20, 2024 · 2c18ca3 · 2c18ca3
2 parents cc15e51 + 2dbfe47
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diff --git a/docs/src/groups/translation.md b/docs/src/groups/translation.md
@@ -1,4 +1,4 @@
-# The Lie group of translations on an Euclidean space
+# The Lie group of translations on a Euclidean space
 
 ```@docs
 TranslationGroup

diff --git a/docs/src/notation.md b/docs/src/notation.md
@@ -13,6 +13,6 @@ For most of the notation used throughout this package, we follow [HilgertNeeb:20
 | ``λ_g: \mathcal G → \mathcal G`` | the left group operation map ``λ_g(h) = g∘h`` | |
 | ``\mathcal M`` | a manifold | ``\mathcal M_1, \mathcal M_2,\ldots,\mathcal N`` | |
 | ``ρ_g: \mathcal G → \mathcal G`` | the right group operation map ``ρ_g(h) = h∘g`` | |
-| ``σ: \mathcal G × \mathcal M`` | a left group action | ``σ_g(p)`` to emphasize a fixed grou pelement |
-| ``τ: \mathcal M × \mathcal G`` | a right group action | ``σ_\mathrm{R}`` | ``τ_g(p)`` o emphasize a fixed grou pelement |
+| ``σ: \mathcal G × \mathcal M`` | a left group action | ``σ_g(p)`` to emphasize a fixed group element |
+| ``τ: \mathcal M × \mathcal G`` | a right group action | ``σ_\mathrm{R}`` | ``τ_g(p)`` to emphasize a fixed group element |
 | ``T_p \mathcal M`` | the tangent space at ``p`` | | |
diff --git a/docs/src/references.md b/docs/src/references.md
@@ -1,7 +1,7 @@
 # Literature
 
 This is all literature mentioned / referenced in the `LieGroups.jl` documentation.
-You find a small reference section at the end of every documentation page
+You can find a small reference section at the end of every documentation page
 that contains the corresponding references as well.
 
 ```@bibliography

diff --git a/src/Lie_algebra/Lie_algebra_interface.jl b/src/Lie_algebra/Lie_algebra_interface.jl
@@ -18,9 +18,9 @@ this is internally just a `const` of the corresponding $(_link(:TangentSpace)).
 
 Return the Lie Algebra belonging to the [`LieGroup`](@ref) `G`.
 """
-const LieAlgebra{𝔽,G,I} = ManifoldsBase.Fiber{
-    𝔽,ManifoldsBase.TangentSpaceType,G,I
-} where {𝔽,G<:LieGroup{𝔽},I<:Identity}
+const LieAlgebra{𝔽,G} = ManifoldsBase.Fiber{
+    𝔽,ManifoldsBase.TangentSpaceType,G,Identity{O}
+} where {𝔽,O<:AbstractGroupOperation,G<:LieGroup{𝔽,O}}
 
 function LieAlgebra(G::LieGroup{𝔽}) where {𝔽}
     return LieAlgebra{𝔽,typeof(G),typeof(Identity(G))}(

diff --git a/src/group_actions/group_operation_action.jl b/src/group_actions/group_operation_action.jl
@@ -209,7 +209,7 @@ Return the inverse of the [`InverseRightGroupOperation`](@ref), that is the [`Ri
 Base.inv(::InverseRightGroupOperation) = RightGroupOperation()
 
 function Base.show(io::IO, A::GroupOperationAction)
-    return print(io, "GroupOperationAction($(A.type),$(A.group))")
+    return print(io, "GroupOperationAction($(A.type), $(A.group))")
 end
 
 """

diff --git a/src/interface.jl b/src/interface.jl
@@ -52,7 +52,7 @@ See also [`identity_element`](@ref) on how to obtain the corresponding [`Abstrac
 
 # Constructors
 
-    Identity(::LieGroup{𝔽,O}) where {𝔽,M,O<:AbstractGroupOperation}
+    Identity(::LieGroup{𝔽,O}) where {𝔽,O<:AbstractGroupOperation}
     Identity(o::AbstractGroupOperation)
     Identity(::Type{AbstractGroupOperation})
 
@@ -126,7 +126,7 @@ function ManifoldsBase.check_point(
 end
 function ManifoldsBase.check_point(
     G::LieGroup{𝔽,O}, e::Identity{O2}; kwargs...
-) where {𝔽,O<:AbstractGroupOperation,O2}
+) where {𝔽,O<:AbstractGroupOperation,O2<:AbstractGroupOperation}
     return DomainError(
         e,
         """