E-theoretic duality for higher rank graph algebras

Popescu, I. and Zacharias, J. (2005) E-theoretic duality for higher rank graph algebras. K-Theory, 34(3), pp. 265-282. (doi:10.1007/s10977-005-5544-6)

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Publisher's URL: http://dx.doi.org/10.1007/s10977-005-5544-6

Abstract

We prove that there is a Poincare type duality in E-theory between higher rank graph algebras associated with a higher rank graph and its opposite correspondent. We obtain an r-duality, that is the fundamental classes are in Er. The basic tools are a higher rank Fock space and higher rank Toeplitz algebra which has a more interesting ideal structure than in the rank 1 case. The K-homology fundamental class is given by an r-fold exact sequence whereas the K-theory fundamental class is given by a homomorphism. The E-theoretic products are essentially pull-backs so that the computation is done at the level of exact sequences.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Zacharias, Dr Joachim
Authors: Popescu, I., and Zacharias, J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:K-Theory
ISSN:0920-3036
ISSN (Online):1573-0514

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