Cyclic Cohomology for Graded $$C^{*,r}$$ C ∗ , r -algebras and Its Pairings with van Daele K-theory
| Autor: | Johannes Kellendonk |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Unital 010102 general mathematics Cyclic homology Subalgebra Statistical and Nonlinear Physics Real structure Invariant (physics) 01 natural sciences Aperiodic graph Pairing 0103 physical sciences Topological invariants 010307 mathematical physics 0101 mathematics Mathematical Physics Mathematics |
| Zdroj: | Communications in Mathematical Physics. 368:467-518 |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-019-03452-1 |
| Popis: | We consider cycles for graded $$C^{*,\mathfrak {r}}$$ -algebras (Real $$C^{*}$$ -algebras) which are compatible with the $$*$$ -structure and the real structure. Their characters are cyclic cocycles. We define a Connes type pairing between such characters and elements of the van Daele K-groups of the $$C^{*,\mathfrak {r}}$$ -algebra and its real subalgebra. This pairing vanishes on elements of finite order. We define a second type of pairing between characters and K-group elements which is derived from a unital inclusion of $$C^*$$ -algebras. It is potentially non-trivial on elements of order two and torsion valued. Such torsion valued pairings yield topological invariants for insulators. The two-dimensional Kane–Mele and the three-dimensional Fu–Kane–Mele strong invariant are special cases of torsion valued pairings. We compute the pairings for a simple class of periodic models and establish structural results for two dimensional aperiodic models with odd time reversal invariance. |
| Databáze: | OpenAIRE |
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