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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Inductive limits of finite dimensional $C^{\ast }$-algebras

Author: Ola Bratteli
Journal: Trans. Amer. Math. Soc. 171 (1972), 195-234
MSC: Primary 46L05
MathSciNet review: 0312282
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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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Keywords: Approximately finite dimensional <!– MATH ${C^ \ast }$ –> <IMG WIDTH="31" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img7.gif" ALT="${C^ \ast }$">-algebras, matrix units, partial embedding, isomorphism, ideal, simple, primitive, factor state, quasi-equivalent representations, permanently locally unitary equivalent embedded, automorphism, unitary operator, pure state, anticommutation relations, current algebra, Fock representation
Article copyright: © Copyright 1972 American Mathematical Society