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.Fil: Ulhoa Coelho, Flavio Ulhoa. Universidade de Sao Paulo; BrasilFil: Platzeck, Maria Ines. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin