(* This is only used in the group ring construction below, as we only have   *)
(* developped the theory of matrix subalgebras for F-algebras.               *)
Definition enveloping_algebra_mx := \matrix_(i < #|G|) mxvec (rG (enum_val i)).
Section Stabiliser.
Variables (m : nat) (U : 'M[R]_(m, n)).
Definition rstab := [set x in G | U *m rG x == U].

Lemma rstab_sub : rstab \subset G.
Canonical rstab_group := Group rstab_group_set.