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• W3100278975 abstract "We consider the functor C that to a unital C*-algebra A assigns the partial order set C(A) of its commutative C*-subalgebras ordered by inclusion. We investigate how some C*-algebraic properties translate under the action of C to order-theoretical properties. In particular, we show that A is finite dimensional if and only C(A) satisfies certain chain conditions. We eventually show that if A and B are C*-algebras such that A is finite dimensional and C(A) and C(B) are order isomorphic, then A and B must be *-isomorphic." @default.
• W3100278975 created "2020-11-23" @default.
• W3100278975 creator A5026900213 @default.
• W3100278975 date "2015-10-19" @default.
• W3100278975 modified "2023-09-27" @default.
• W3100278975 title "Classifying Finite-Dimensional C*-Algebras by Posets of Their Commutative C*-Subalgebras" @default.
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• W3100278975 doi "https://doi.org/10.1007/s10773-015-2817-6" @default.
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