Exterior power streamlining

[HechtiDerLachs]

This removes induced_map_on_exterior_power and replaces it by exterior_power. Taking exterior powers is a functor, so it should be applicable to maps directly.

Another family of methods which are now deprecated is hom(::Obj, ::Obj, ::Morphism) which checks whether the first two arguments are exterior powers of the domain and codomain of the morphism, respectively, and then computes the induced map. Introducing this was probably never a clever idea and should not have happend imho.

[lgoettgens]

I am neither in favor of nor objecting to this PR. My contribution to this PR is purely to keep the LieAlgebraModules consistent with FreeMod.
I also introduced deprecations for changes in the experimental "LieAlgebras", since I have personal code outside of Oscar, that uses these functions, which I would like not to break.

[fieker]

On Wed, Jan 14, 2026 at 07:16:45AM -0800, Lars Göttgens wrote: lgoettgens left a comment (oscar-system/Oscar.jl#5702) I am neither in favor of nor objecting to this PR. My contribution to this PR is purely to keep the LieAlgebraModules consistent with FreeMod. I also introduced deprecations for changes in the experimental "LieAlgebras", since I have personal code outside of Oscar, that uses these functions, which I would like not to break.

I know this .... very well... Fun question: exterior_power(hom): how does this interact with caching of structures? Using tensor_product(hom, hom) has the same problem: it need to create the tensor_products of the domains/ codomains... I agree with the maths, but what about the cached structures?

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[HechtiDerLachs]

I agree with the maths, but what about the cached structures?

For the modules the exterior powers are usually cached in the original module; unless they are created with cached = false. The call to exterior_power(::Morphism, ::p) then recreates (or loads from cache) the exterior powers of domain and codomain. If they are created at this point, they are cached by default. Maybe one should allow to disable this, too?

Either way, the user may specify their own domain and codomain to be used for the result. In that case, they need to be compatible with the provided map, of course.

[HechtiDerLachs]

@lgoettgens : One test in experimental/LieAlgebras/test/LieAlgebraModuleHom-test.jl still fails. Other than that this should be good to go.