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ON THE EVANS CHAIN COMPLEX

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  14 October 2024

S. JOSEPH LIPPERT Open the ORCID record for S. JOSEPH LIPPERT [Opens in a new window]
S. JOSEPH LIPPERT*
Affiliation:
Department of Mathematics and Statistics, Sam Houston State University, Huntsville, Texas 77341, USA
*
e-mail: [email protected]
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Abstract

We elaborate on the construction of the Evans chain complex for higher-rank graph $C^*$-algebras. Specifically, we introduce a block matrix presentation of the differential maps. These block matrices are then used to identify a wide family of higher-rank graph $C^*$-algebras with trivial K-theory. Additionally, in the specialised case where the higher-rank graph consists of one vertex, we are able to use the Künneth theorem to explicitly compute the homology groups of the Evans chain complex.

Keywords

operator algebrashigher-rank graphsK-theoryspectral sequences

MSC classification

Primary: 46L80: $K$-theory and operator algebras (including cyclic theory)
Secondary: 46L37: Subfactors and their classification
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 11
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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