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On the \(C^*\)-algebraic approach to topological phases for insulators. (English) Zbl 1382.82045
The \(C^*\)-algebraic approach to topological insulators is based on the non-commutative topology of the \(C^*\)-algebra of observables of the insulator in the one-particle approximation. The author relates the symmetries of insulators to graded real structures on the observable \(C^*\)-algebra and classifies the topological phases using A. van Daele’s formulation of \(K\)-theory [Q. J. Math., Oxf. II. Ser. 39, No. 154, 185–199 (1988; Zbl 0657.46050)].

MSC:
82D20 Statistical mechanical studies of solids
81V70 Many-body theory; quantum Hall effect
46L80 \(K\)-theory and operator algebras (including cyclic theory)
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