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 (1998)

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by S. C. Power

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8 - 2 self

BibTeX

@MISC{Power98homologyfor,
    author = {S. C. Power},
    title = {Homology for Operator Algebras III: Partial Isometry Homotopy and Triangular Algebras},
    year = {1998}
}

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Abstract

The partial isometry homology groups Hn 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 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 (\Delta(G))\Omega Z K0 (C (A)) and CHn (A(G) ? A) is the simplicial homology group Hn (\Delta(G); K 0 (C (A))) with coefficients in K0 (C (A)).

Keyphrases

partial isometry homotopy triangular algebra operator algebra iii cuntz algebra regular inclusion digraph algebra various triangular operator algebra omega k0 simplicial homology group hn equivalence class stable algebra partial isometry homology hn lexicographic product disc algebra simplicial homotopy reduction cuntz algebra om partial isometry chain complex homology partial isometry homology group hn triangular subalgebra related chain complex homology ch

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