Free \(W^*\)-dynamical systems from \(p\)-adic number fields and the Euler totient function (Q901464)
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scientific article; zbMATH DE number 6528864
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Free \(W^*\)-dynamical systems from \(p\)-adic number fields and the Euler totient function |
scientific article; zbMATH DE number 6528864 |
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Free \(W^*\)-dynamical systems from \(p\)-adic number fields and the Euler totient function (English)
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12 January 2016
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Summary: In this paper, we study relations between free probability on crossed product \(W^*\)-algebras with a von Neumann algebra over \(p\)-adic number fields \(\mathbb Q_p\) (for primes \(p\)), and free probability on the subalgebra \(\Phi\), generated by the Euler totient function \(\phi\), of the arithmetic algebra \(\mathcal A\), consisting of all arithmetic functions. In particular, we apply such free probability to consider operator-theoretic and operator-algebraic properties of \(W^*\)-dynamical systems induced by \(\mathbb Q_p\) under free-probabilistic (and hence, spectral-theoretic) techniques.
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\(p\)-adic number fields \(\mathbb Q_p\)
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\(p\)-adic von Neumann algebras \(\mathfrak M_p\)
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dynamical systems induced by \(\mathbb Q_p\)
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arithmetic functions
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arithmetic algebra \(\mathcal A\)
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Euler totient function \(\phi\)
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