Residually finite dimensional and AF-embeddable C∗-algebras, peprint

Abstract. We show that every separable nuclear residually nite dimensional C-algebras satisfying the Universal Coecient Theorem can be embedded into a unital separable simple AF-algebra. The problem of determining when a C-algebra can be embedded as a C-subalgebra of an AF-algebra has been studied for a while (for example, in [Pi], [Vo], [Sp], [Br] and [D] | to name a few). J. Spielberg showed in [Sp], among other related things, that every separable CCR C-algebra can be embedded into an AF-algebra. In [D], it is shown that a separable nuclear residually nite dimensional C-algebra can be embedded into an AF-algebra if it is homotopically dominated by an AF-algebra. Consequently, from a result of Spielberg, Dadarlat shows (in [D]) that the AF-embeddability of a residually nite dimensional C-algebra A (say in the \bootstrap " class of [RS]) depends only on the homotopy type of A: The renewed interest in residually nite dimensional C-algebras arises from the result of Blackadar and Kirchberg ([BK1] and [BK2]) that simple separable nuclear quasidiagonal C-algebras are inductive limits of nuclear RFD C-algebras