add check_commutative_group_algebra to check whether Group Algebra is Commutative, L(a) = R(a)

[Fe-r-oz]

This PR implements a method to check whether group algebra is commutative, $L(a) = R(a)$. This check is inspired from the Appendix B of this paper and will be used when working with non-abelian groups.

Abelian Groups

julia> using Oscar

julia> G = cyclic_group(6);

julia> GA = group_algebra(GF(2), G);

julia> a = rand(GA);

julia> L_a = representation_matrix(a);

julia> R_a = representation_matrix(a, :right);

julia> L_a == R_a
true

Non-Abelian Groups

julia> using Oscar

julia> G = dihedral_group(6);

julia> GA = group_algebra(GF(2), G);

julia> a = rand(GA);

julia> L_a = representation_matrix(a);

julia> R_a = representation_matrix(a, :right);

julia> L_a == R_a
false

Related Issue: #446

• The code is properly formatted and commented.
• Substantial new functionality is documented within the docs.
• All new functionality is tested.
• All of the automated tests on github pass.
• We recently started enforcing formatting checks. If formatting issues are reported in the new code you have written, please correct them.

[Fe-r-oz]

Hecke has the is_commutative method, so we don't need to manually check $L(a) = R(a)$.

is_commutative: https://github.com/thofma/Hecke.jl/blob/e76d83a97bf3e70437f37701d1e98703d0d68642/src/AlgAss/AlgGrp.jl#L131

Abeian groups

julia> using Hecke: is_commutative

julia> using Oscar

julia> G = cyclic_group(6);

julia> GA = group_algebra(GF(2), G);

julia>  is_commutative(GA)
true

Non-abelian

julia> using Hecke: is_commutative

julia> using Oscar

julia> G = dihedral_group(6);

julia> GA = group_algebra(GF(2), G);

julia> is_commutative(GA)
false