Automatically assigned DDC number:
Manually assigned DDC number: 51424
Title: Homology for Operator Algebras III: Partial Isometry Homotopy and Triangular Algebras
Subject: S. C. Power Homology for Operator Algebras III: Partial Isometry Homotopy and Triangular Algebras
Description: . The partial isometry homology groups Hn defined in Power  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)). Contents 1. The Partial Isometry Homology Hn (A; C) 37 2. Vanishing Homology 40 3. The Proof of Theorem 1 43 4. K 0 -regular Inclusion and Homotopy 44 5. The Cuntz Algebras and TOm 45 6. The Proof of Theorem 2 48 7. The Partial Isometry Chain Complex Homology 51 References 56 Taking the perspective that equivalence classes of projections in the stable algebra of a non-se...
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