diff --git a/src/Lie_algebra/Lie_algebra_interface.jl b/src/Lie_algebra/Lie_algebra_interface.jl
index 25a9748..1cf67bb 100644
--- a/src/Lie_algebra/Lie_algebra_interface.jl
+++ b/src/Lie_algebra/Lie_algebra_interface.jl
@@ -18,14 +18,12 @@ 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}
-
-function LieAlgebra(G::LieGroup{𝔽}) where {𝔽}
-    return LieAlgebra{𝔽,typeof(G),typeof(Identity(G))}(
-        G, Identity(G), ManifoldsBase.TangentSpaceType()
-    )
+const LieAlgebra{𝔽,O<:AbstractGroupOperation,G<:LieGroup{𝔽,O}} = ManifoldsBase.Fiber{
+    𝔽,ManifoldsBase.TangentSpaceType,G,Identity{O}
+}
+
+function LieAlgebra(G::LieGroup{𝔽,O}) where {𝔽,O<:AbstractGroupOperation}
+    return LieAlgebra{𝔽,O,typeof(G)}(G, Identity(G), ManifoldsBase.TangentSpaceType())
 end
 
 _doc_lie_bracket = """
diff --git a/src/group_operations/addition.jl b/src/group_operations/addition.jl
index 049ca1c..a725801 100644
--- a/src/group_operations/addition.jl
+++ b/src/group_operations/addition.jl
@@ -166,8 +166,8 @@ function inv!(G::LieGroup{𝔽,AdditionGroupOperation}, h, g) where {𝔽}
 end
 
 _doc_lie_bracket_add = """
-    lie_bracket!(𝔤::LieAlgebra{𝔽,<:LieGroup{𝔽,AdditionGroupOperation}}, X, Y)
-    lie_bracket!(𝔤::LieAlgebra{𝔽,<:LieGroup{𝔽,AdditionGroupOperation}}, Z, X, Y)
+    lie_bracket!(𝔤::LieAlgebra{𝔽,AdditionGroupOperation}, X, Y)
+    lie_bracket!(𝔤::LieAlgebra{𝔽,AdditionGroupOperation}, Z, X, Y)
 
 Compute the Lie bracket ``[⋅,⋅]: $(_math(:𝔤))×$(_math(:𝔤)) → $(_math(:𝔤))``,
 which for the for the [`AdditionGroupOperation`](@ref) simplifies to the
@@ -176,12 +176,10 @@ The computation can be done in-place of `Z`.
 """
 
 @doc "$(_doc_lie_bracket_add)"
-lie_bracket(𝔤::LieAlgebra{𝔽,<:LieGroup{𝔽,AdditionGroupOperation}}, X, Y) where {𝔽}
+lie_bracket(𝔤::LieAlgebra{𝔽,AdditionGroupOperation}, X, Y) where {𝔽}
 
 @doc "$(_doc_lie_bracket_add)"
-function lie_bracket!(
-    𝔤::LieAlgebra{𝔽,<:LieGroup{𝔽,AdditionGroupOperation}}, Z, X, Y
-) where {𝔽}
+function lie_bracket!(𝔤::LieAlgebra{𝔽,AdditionGroupOperation}, Z, X, Y) where {𝔽}
     return zero_vector!(𝔤, Z)
 end