Matrix descriptions of even-dimensional fuzzy spherical branes S 2 k in Matrix Theory and other contexts in type II superstring theory reveal, in the large N limit, higher-dimensional geometries SO(2 k+1)/ U( k), which have an interesting spectrum of SO(2 k+1) harmonics and can be up to 20-dimensional, while the spheres are restricted to be of dimension less than 10. In the case k=2, the matrix description has two dual field theory formulations. One involves a field theory living on the non-commutative coset SO(5)/ U(2) which is a fuzzy S 2 fibre bundle over a fuzzy S 4. In the other, there is a U( n) gauge theory on a fuzzy S 4 with O(n 3) instantons. The two descriptions can be related by exploiting the usual relation between the fuzzy two-sphere and U( n) Lie algebra. We discuss the analogous phenomena in the higher-dimensional cases, developing a relation between fuzzy SO(2 k)/ U( k) cosets and unitary Lie algebras.