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arXiv · 1802.02487

Invariant states on noncommutative tori

Federico Bambozzi·Simone Murro·Nicola Pinamonti
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Abstract

For any number $h$ such that $\hbar:=h/2π$ is irrational and any skew-symmetric, non-degenerate bilinear form $σ:\mathbb{Z}^{2g}\times \mathbb{Z}^{2g} \to \mathbb{Z}$, let be $\mathcal{A}^h_{g,σ}$ be the twisted group $*$-algebra $\mathbb{C}[\mathbb{Z}^{2g}]$ and consider the ergodic group of $*$-automorphisms of $\mathcal{A}^h_{g,σ}$ induced by the action of the symplectic group Sp$(\mathbb{Z}^{2g},σ)$. We show that the only Sp$(\mathbb{Z}^{2g},σ)$-invariant state on $\mathcal{A}^h_{g,σ}$ is the trace state $τ$.

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BibTeXRIS

Federico Bambozzi, Simone Murro, Nicola Pinamonti. 2019-07-04. Invariant states on noncommutative tori. https://doi.org/10.1093/imrn%2Frnz189

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