Isometric dilations of non-commuting finite rank n-tuples

A contractive n-tuple A = (A(1),...,A(n)) has a minimal joint isometric dilation S = (S-1,...,S-n) where the Si's are isometries with pairwise orthogonal ranges. This determines a representation of the Cuntz-Toeplitz algebra. When A acts on a finite dimensional space, the wot-closed nonself-adjoint algebra G generated by S is completely described in terms of the properties of A. This provides complete unitary invariants for the corresponding representations. In addition, we show that the algebra G is always hyper-reflexive. In the last section. we describe similarity invariants. In particular, an n-tuple B of d x d matrices is similar to an irreducible ti-tuple A if and only ifa certain finite set of polynomials vanish on B.