Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Homology for operator algebras III: partial isometry homotopy and triangular algebras.
AU - Power, Stephen C.
PY - 1998/3/6
Y1 - 1998/3/6
N2 - The partial isometry homology groups Hn dened in Power [1] 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((G))ZK0(C(A)) and CHn(A(G) ? A) is the simplicial homology group Hn((G);K0(C(A))) with coecients in K0(C(A)).
AB - The partial isometry homology groups Hn dened in Power [1] 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((G))ZK0(C(A)) and CHn(A(G) ? A) is the simplicial homology group Hn((G);K0(C(A))) with coecients in K0(C(A)).
M3 - Journal article
VL - 4
SP - 35
EP - 56
JO - New York Journal of Mathematics
JF - New York Journal of Mathematics
SN - 1076-9803
ER -