Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 531, Issue 2, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2023.127827
Keywords
Extension; K-homology; K-group; Toeplitz algebra; Cuntz-Krieger algebra; C*-algebra
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We introduce the concept of K-theoretic duality for extensions of separable unital nuclear C*-algebras, using the K-homology long exact sequence and cyclic six term exact sequence for K-theory groups of extensions. We then prove that the Toeplitz extension tau A of a Cuntz-Krieger algebra OA is the K-theoretic dual of the Toeplitz extension tau At of the Cuntz-Krieger algebra OAt for the transposed matrix At of A. As an application, we show that if the Toeplitz algebras TAt and TBt of the transposed matrices are isomorphic, then the Toeplitz algebras TA and TB themselves are isomorphic as C*-algebras.
We introduce the notion of K-theoretic duality for extensions of separable unital nuclear C*-algebras by using K-homology long exact sequence and cyclic six term exact sequence for K-theory groups of extensions. We then prove that the Toeplitz extension tau A of a Cuntz-Krieger algebra OA is the K-theoretic dual of the Toeplitz extension tau At of the Cuntz-Krieger algebra OAt for the transposed matrix At of A. A pair of isomorphic Cuntz-Krieger algebras OA and OB does not necessarily yield the isomorphic pair of OAt and OBt. However, as an application, we may show that two Toeplitz algebras TA and TB are isomorphic as C*-algebras if and only if the Toeplitz algebras TAt and TBt of their transposed matrices are isomorphic. (c) 2023 Elsevier Inc. All rights reserved.
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