Inductive limits of finite dimensional 𝐶*-algebras

Abstract

Inductive limits of ascending sequences of finite dimensional C ∗ {C^ \ast } -algebras are studied. The ideals of such algebras are classified, and a necessary and sufficient condition for isomorphism of two such algebras is obtained. The results of Powers concerning factor states and representations of UHF-algebras are generalized to this case. A study of the current algebra of the canonical anticommutation relations is then being made.