 

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 


Abstract
The partial isometry homology
groups H_{n} 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 Ktheory. Simplicial homotopy reductions are used
to identify both H_{n} and CH_{n} for the lexicographic products
A(G) ★ A with A(G) a digraph algebra and A a triangular
subalgebra of the Cuntz algebra O_{m}. Specifically
H_{n} (A(G) ★ A) = H_{n} (Δ (G)) ⊗_{Z} K_{0} (C*(A))
and CH_{n} (A(G) ★ A) is the simplicial homology group
H_{n} (Δ (G) ; K_{0} (C*(A))) with coefficients in K_{0} (C*(A)).


Author information
Department of Mathematics and Statistics, Lancaster University, England
http://www.maths.lancs.ac.uk/~power/

