An equivariant pullback structure of trimmable graph C'-algebras

To unravel the structure of fundamental examples studied in noncommutative topology, we prove that the graph C*-algebra C*(E) of a trimmable graph E is U(1)-equivariantly iso-morphic to a pullback C *-algebra of a subgraph C *-algebra C*(E'') and the C *-algebra of func-tions on a circle tensored with another subgraph C*-algebra C*(E'). This allows us to approach the structure and K-theory of the fixed-point subalgebra C*(E)U .1/ through the (typically simpler) C *-algebras C*(E'), C*(E'') and C*(E'')U.1/. As examples of trimmable graphs, we consider one-loop extensions of the standard graphs encoding respectively the Cuntz algebra O2 and the Toeplitz algebra T . Then we analyze equivariant pullback structures of trimmable graphs yielding the C*-algebras of the Vaksman-Soibelman quantum sphere S2n+1 q and the quantum lens space L3 q(l;1, l), respectively.