An equivariant pullback structure of trimmable graph C*-algebras

2017/12/21 by Arici, Francesca, D'Andrea, Francesco, Hajac, Piotr M. +1 · 2 citations
#46L80 #46L85 (Primary) #58B32 (Secondary) #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1712.08010

Abstract

We prove that the graph C*-algebra C^*(E) of a trimmable graph E is U(1)-equivariantly isomorphic to a pullback C*-algebra of a subgraph C*-algebra C^*(E'') and the C*-algebra of functions on a circle tensored with another subgraph C*-algebra C^*(E'). This allows us to unravel 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 L_q³(l; 1,l), respectively.

Cited by

• Milnor meets Hopf and Toeplitz at the K-theory of quantum projective planes
• On amplified graph C*-algebras as cores of Cuntz-Krieger algebras

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