\(E\)-theoretic duality for higher rank graph algebras (Q2576460)

In [\textit{J.~Kaminker} and \textit{I.~Putnam}, Commun.\ Math.\ Phys.\ 187, 509--522 (1977; Zbl 0887.19002)], a Poincaré type duality between Cuntz--Krieger algebras \(O_A\) and \(O_{A^T}\) in \(K\)-theory was exhibited, where \(A^T\) is the transpose of \(A\). The present paper generalizes this duality for higher rank graph algebras. Let \(O_\Lambda\) and \(O_{\Lambda^{\text{op}}}\) be the higher rank graph algebras defined by the rank \(r\) graph \(\Lambda\) and its opposite correspondent \(\Lambda^{\text{op}}\). The authors construct the fundamental classes \(\Delta\in E^r(O_\Lambda\otimes O_{\Lambda^{\text{op}}},\mathbb C)\) and \(\delta\in E^r(\mathbb C,O_\Lambda\otimes O_{\Lambda^{\text{op}}})\) and check that these two classes induce a Poincaré type duality in \(E\)-theory.