2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94761For any finite dimensional C^*-algebra A, we give an endomorphism Φof the hyperfinite II_1 factor R of finite Jones index such that: for all k \in \mathbb {N}, Φ^k (R)' \cap R= \otimes^k A. The Jones index [R: Φ(R)]= (rank (A))^2, here rank (A) is the dimension of the maximal abelian subalgebra of A.Operator AlgebrasFunctional Analysis46L37; 47B47text