On the representation dimension of some classes of algebras

We show that the representation dimension of the following classes of algebras is at most 3: (a) Artin algebras A such that the functor HomA(D(A),−) has finite length (or dually, HomA(−,A) has finite length). These algebras coincide with the right (left) glued algebras, as introduced in [I. Assem, F.U. Coelho, J. Pure Appl. Algebra 96 (3) (1994) 225]; and (b) Trivial extensions of iterated tilted algebras.