Power, Stephen C. (1998) *Homology for operator algebras III: partial isometry homotopy and triangular algebras.* New York Journal of Mathematics, 4. pp. 35-56. ISSN 1076-9803

## 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)).

Item Type: | Article |
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Journal or Publication Title: | New York Journal of Mathematics |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 19440 |

Deposited By: | ep_ss_importer |

Deposited On: | 13 Nov 2008 11:22 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 09 Oct 2013 13:12 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/19440 |

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