Observables Algebras for Solid State Systems
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This chapter introduces the C\(^*\)-algebras of bulk, half-space and boundary observables, together with their canonical representations which generate the physical models for topological insulators presented in Chap. 2. Then the exact sequence connecting these algebras is discussed. In particular, it is shown to be isomorphic to the Pimsner-Voiculescu exact sequence. This chapter also introduces the non-commutative analysis tools and the smooth sub-algebras to be used in the remainder of the book.