  Given a representation V of a group G, there are two natural ways of defining
a representation of the group algebra k[G] in the external power V^{\wedge m}.
The set L(V) of elements of k[G] for which these two ways give the same result
is a Lie algebra and a representation of G. For the case when G is a symmetric
group and V = C^n, a permutation representation, these spaces L(C^n) are
naturally embedded into one another. We describe L(C^n) for small n and
formulate some questions and conjectures.
  This is a note on research in progress.
