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

Research output: Contribution to journal › Journal article › peer-review

Power, SC 1998, 'Homology for operator algebras III: partial isometry homotopy and triangular algebras.', *New York Journal of Mathematics*, vol. 4, pp. 35-56. <http://www.emis.de/journals/NYJM/j/1998/4-4.html>

Power, S. C. (1998). Homology for operator algebras III: partial isometry homotopy and triangular algebras. *New York Journal of Mathematics*, *4*, 35-56. http://www.emis.de/journals/NYJM/j/1998/4-4.html

Power SC. Homology for operator algebras III: partial isometry homotopy and triangular algebras. New York Journal of Mathematics. 1998 Mar 6;4:35-56.

@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",

}

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 -