New York Journal of Mathematics
Volume 4 (1998) 35-56


S. C. Power

Homology for Operator Algebras III: Partial Isometry Homotopy and Triangular Algebras

Published: March 6, 1998
Keywords: operator algebra, homology group, nonselfadjoint, Cuntz algebra
Subject: 47D25, 46K50

The partial isometry homology groups Hn defined in Power [17] and a related chain complex homology CH* are calculated for various triangular operator algebras, including the disc algebra. These invariants are closely connected with K-theory. Simplicial homotopy reductions are used to identify both Hn and CHn for the lexicographic products A(G) ★ A with A(G) a digraph algebra and A a triangular subalgebra of the Cuntz algebra Om. Specifically Hn (A(G) ★ A) = Hn (Δ (G)) ⊗Z K0 (C*(A)) and CHn (A(G) ★ A) is the simplicial homology group Hn (Δ (G) ; K0 (C*(A))) with coefficients in K0 (C*(A)).

Author information

Department of Mathematics and Statistics, Lancaster University, England