Inductive limits of finite dimensional 𝐶*-algebras

Bratteli, Ola

doi:10.1090/S0002-9947-1972-0312282-2

Inductive limits of finite dimensional $C^{\ast }$-algebras
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Trans. Amer. Math. Soc. 171 (1972), 195-234 Request permission

Abstract:

Inductive limits of ascending sequences of finite dimensional ${C^ \ast }$-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.

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