A construction of split exact sequences for amplified graph C*-algebras with sinks yields explicit KK-equivalences to C^N for a broad class including the quantum Grassmannian Gr_q(2,4) and an equivalence between CP^1 and CP_q^1.
G.The operator K-functor and extensions of C*-algebras.Mathematics of the USSR- Izvestiya 16, 3 (Jun 1981), 513–572
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On split exact sequences and KK-equivalences of amplified graph C*-algebras
A construction of split exact sequences for amplified graph C*-algebras with sinks yields explicit KK-equivalences to C^N for a broad class including the quantum Grassmannian Gr_q(2,4) and an equivalence between CP^1 and CP_q^1.