Inductive limits of finite dimensional 𝐶*-algebras

Abstract

Inductive limits of ascending sequences of finite dimensional <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Superscript asterisk"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>C</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{C^ \ast }</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-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.