K-Theory for Topological Solid State Systems

Part of the Mathematical Physics Studies book series (MPST)


The first part of the chapter reviews the K-theory of unital and non-unital C\(^*\)-algebras, particularly, the K-groups and their standard characterization, the six-term exact sequences and their connecting maps as well as the suspensions and Bott periodicity. In the second part, the analysis is specialized to the observable algebras defined in Chap.  3. Using the Pimsner-Voiculescu sequence, this allows to present the generators of the K-groups in detail. In the third part, various connecting maps for solid state systems are computed explicitly.


Solid State Systems Pimsner Voiculescu Connectivity Map Bott Periodicity Fermi Projection 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Physics DepartmentYeshiva UniversityNew YorkUSA
  2. 2.Department MathematikFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

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