On the normalizer of the reflexive cover of a unital algebra of linear transformations

Given a unital algebra A of linear transformations on finite-dimensional complex vector space V, in this paper we study the set Col(A) consisting those invertible S V which map every subspace M∈Lat(A) to SM∈Lat(A). We show that is normalizer group reflexive cover A. For (A) generated by transformation A, give complete description Col(A). By using primary decomposition first reduce problem characterizing Col(N) given nilpotent N. While always contains all commutant (N)′ N, it contained (N)′. prove proper subgroup (AlgLat(N)′)−1 if and only at least two Jordan blocks N are dimension 2 or more. also determine Col(J2⊕J2).