A dual graph construction for higher-rank graphs, and 𝐾-theory for finite 2-graphs
Copyright policy )A dual graph construction for higher-rank graphs, and 𝐾-theory for finite 2-graphs
Given a k k -graph Λ \Lambda and an element p p of N k \mathbb {N}^k , we define the dual k k -graph, p Λ p\Lambda . We show that when Λ \Lambda is row-finite and has no sources, the C ∗ C^* -algebras C ∗ ( Λ ) C^*(\Lambda ) and C ∗ ( p Λ ) C^*(p\Lambda ) coincide. We use this isomorphism to apply Robertson and Steger’s results to calculate the K K -theory of C ∗ ( Λ ) C^*(\Lambda ) when Λ \Lambda is finite and strongly connected and satisfies the aperiodicity condition.
- University of Wollongong Australia
- University of Newcastle Australia Australia
construction, 46L05, dual, 2, k, Science and Technology Studies, K-theory, C*-algebra, Engineering, graphs as categories, FOS: Mathematics, finite, cuntz-krieger algebras, theory, Operator Algebras (math.OA), graph algebra, higher, graphs, Mathematics - Operator Algebras, \(K\)-theory and operator algebras (including cyclic theory), graph, c-asterisk-algebras, infinite-graphs, General theory of \(C^*\)-algebras, rank
construction, 46L05, dual, 2, k, Science and Technology Studies, K-theory, C*-algebra, Engineering, graphs as categories, FOS: Mathematics, finite, cuntz-krieger algebras, theory, Operator Algebras (math.OA), graph algebra, higher, graphs, Mathematics - Operator Algebras, \(K\)-theory and operator algebras (including cyclic theory), graph, c-asterisk-algebras, infinite-graphs, General theory of \(C^*\)-algebras, rank
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