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Homology for operator algebras III: partial isometry homotopy and triangular algebras.

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Homology for operator algebras III: partial isometry homotopy and triangular algebras. / Power, Stephen C.

In: New York Journal of Mathematics, Vol. 4, 06.03.1998, p. 35-56.

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@article{bf100af2c45847048800430d509f4980,
title = "Homology for operator algebras III: partial isometry homotopy and triangular algebras.",
abstract = "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)).",
author = "Power, {Stephen C.}",
year = "1998",
month = mar,
day = "6",
language = "English",
volume = "4",
pages = "35--56",
journal = "New York Journal of Mathematics",
issn = "1076-9803",
publisher = "Electronic Journals Project",

}

RIS

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 -